Sergey V. Lototsky

Department of Mathematics
University of Southern California
3620 S. Vermont Avenue, KAP 108
Los Angeles, CA 90089-2532
tel.: 213--740-2389, fax: 213--740-2424,
e-mail: lototsky (at) usc (dot) edu

CURRENT POSITION: Professor, Department of Mathematics , University of Southern California, Los Angeles, CA.

PREVIOUS POSITIONS AND APPOINTMENTS:

• May 15, 2003 - December 22, 2006, Associate Professor, Department of Mathematics, University of Southern California, Los Angeles, CA.
• September 1, 1998 - May 15, 2003, Assistant Professor, Department of Mathematics, University of Southern California, Los Angeles, CA (on leave at MIT during 1998-1999 and 1999-2000 school years).
• September 1, 1997 - July 31, 2000, C.L.E. Moore Instructor of Mathematics, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA.
• September 1, 1996 - August 22, 1997, Post-doctoral member of the Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN.

VISITING POSITIONS:

• September-December 2007, Institut Mittag-Leffler, The Royal Swedish Academy of Sciences.
• February-April 2007, Visiting Professor, Division of Applied Mathematics, Brown University, Providence, RI.
• July-August 1999, Visiting Scholar (participant in the Summer Program in Probability), Center for Mathematical Sciences, University of Wisconsin, Madison, WI.

EDUCATION:

• Ph. D. (Applied Mathematics) - August 1996, University of Southern California. Adviser: B. L. Rozovskii.
• M. Sc. (Physics) - June 1992, Moscow Institute of Physics and Technology, Moscow, Russia. Adviser: R. Sh. Liptser.

AWARDS

• NSF Grant DMS-0803378.
  Date of award: June 9, 2008.
  Title: Stochastic Partial Differential Equations: Theory and Applications.
  Continuing 4-year grant totaling $180,000.
• NSF CAREER award DMS-0237724.
  Date of award: February 28, 2003.
  Title: Stochastic Partial Differential Equations and Applications.
  Continuing 5-year grant totaling $400,000.
• Sloan Research Fellowship.
  Dates of Award: September 16, 2002 through September 15, 2004.
  Amount: $40,000. (Extended to September 15, 2006)
• ARO grant DAAD19-02-1-0374 (Co-PI with B. Rozovskii).
  Dates of award: September 1, 2002 through August 31, 2005. Title: Numerical Methods and Statistical Inference for Complex Stochastic Systems.
  Total Amount: $150,000.
• Research contract "Target Scene Resolution and Calibration", Scientific Systems Company, Inc. (Sub-contract for Army STTR Phase I under contract W9113M-04-P-0146.)
  Dates of Award: August 19, 2004 through February 18, 2005.
  Amount: $29,400.
• NSF Grant DMS-9972016.
  Dates of Award: July 01, 1999 through February 28, 2002.
  Title: Boundary Value Problems for Stochastic Parabolic Equations.
  Amount: $61,000.
• NRC COBASE Travel Grant.
  Dates of Award: February 1, 2003 through August 31, 2003.
  Amount: $5300 (returned unspent for technical reasons).
• Travel Grant to attend Fifteenth International Symposium on Mathematical Theory of Networks and Systems, University of Notre Dame, August 12-16, 2002.
• Travel Grant to attend the conference in honor of Harry Kesten, Cornell University, June 27-July 1, 1998.
• Master of Science (Physics) Diploma with Honors, Moscow Institute of Physics and Technology, 1992.

RESEARCH INTERESTS:

• Probability Theory and Stochastic Processes
• Stochastic Partial Differential Equations
• Statistical Inference for Stochastic Processes
• Nonlinear Filtering
• Numerical Methods for Partial Differential Equations
• Mathematical Finance

TEACHING

• Curriculum development: Seminar in problem solving (MATH 395), co-developed with R. Arratia, first implemented in Spring 2006.
• Special topics classes taught at USC:
  MATH 705 (Seminar in Probability): Spring and Fall 2010, Spring and Fall 2011.
  MATH 681 (Selected Topics in Functional Analysis): Malliavin Calculus, Summer 2011.
  MATH 625 (Topics in Analysis): Function Spaces and Interpolation, Fall 2003.
  MATH 605 (Topics in Probability): Large Deviations (Spring 2011), Ergodicity in Infinite-Dimensional Stochastic Evolution Systems (Fall 2010), Introduction to Stochastic Partial Differential Equations (Spring 2005, Spring 2009); Introduction to Stochastic Optimal Control, Summer 2008.
  MATH 500 (graduate seminar on current developments in mathematics), organizer in Spring and Fall 2003; co-organizer in Fall 2002, Spring 2006.
• Regular classes taught at USC:
  MATH 601 (Optimization Theory and Techniques): Spring 2010.
  MATH 555a (Graduate Partial Differential Equations): Fall 2000.
  MATH 508 (Filtering Theory): Spring 2008, Spring 2009, Spring 2011.
  MATH 445 (Mathematics of Physics and Engineering, II): Fall 2001, Fall 2005, Fall 2009.
  MATH 407 (Probability Theory): Fall 2008, Fall 2009.
  MATH 226 (Multi-variable Calculus): Fall 2000, Fall 2001.
  MATH 218 (Probability for Business): Spring 2001, Fall 2002, Spring 2003, Spring 2005.
  MATH 126 (Second-semester Calculus): Fall 2006 (two sections), Spring 2008, Fall 2011 (two sections).
  MATH 125 (First-semester Calculus): Spring 2002.
  MATH 118x (Fundamental Principles of Calculus: Lecture/Discussion combo): Spring 2006.
• Teaching at MIT:
  18.100A (Introduction to Analysis): Spring 2000.
  18.03 (Differential Equations): Spring 1998, Spring 1999.
  18.02 (Freshmen multi-variable calculus): Fall 1998 and Spring 2000.
  18.01A/02A (Freshmen one- and multi-variable calculus): Fall 1997, Fall 1999.
• Teaching Assistant at USC:
  MATH 445 (Mathematics of Physics and Engineering, II): Fall 1995 and Spring 1996.
  MATH 245 (Mathematics of Physics and Engineering I): Spring 1995.
  MATH 226 (Calculus III): Fall 1993, Spring and Fall 1994.
• Teaching buy-out through the Sloan Research Fellowship: two courses in Spring and Fall of 2004; one course in Fall 2005.
• Sabbatical leaves:
  Spring and Fall 2007.

PROFESSIONAL SERVICES

• Conferences
  1. "Inverse Problems in Stochastic Differential Equations" USC, May 22-26, 2007: Organizer.
  2. "Random Media and Stochastic Partial Differential Equations" USC, June 14-18, 2005: Organizer.
  3. AIMS Fifth International Conference on Dynamical Systems and Differential Equations, CalPoly, Pomona, June 16-19, 2004: A special session organizer.
• Technical reviewer for the journals
  1. Annals of Probability
  2. Annals of Applied Probability
  3. Bernoulli
  4. Canadian Journal of Physics
  5. Communications on Stochastic Analysis
  6. Computers and Mathematics
  7. Electronic Journal of Probability
  8. European Physics Letters
  9. Forum Mathematicum
  10. IEEE Transactions on Automatic Control
  11. Indiana University Mathematics Journal
  12. Inventiones Mathematicae
  13. International Journal of Control
  14. International Journal of Mathematics and Mathematical Sciences
  15. International Journal of Stochastic Analysis
  16. Journal of Mathematical Analysis and Applications
  17. Journal of Nonlinear Analysis - A
  18. Journal of Theoretical Probability
  19. Multiscale Modeling and Simulation
  20. Potential Analysis
  21. Probability Theory and Related Fields
  22. Quarterly of Applied Mathematics
  23. SIAM Journal on Computing
  24. SIAM Journal on Control and Optimization
  25. SIAM Journal on Imaging Sciences
  26. SIAM Journal on Mathematical Analysis
  27. SIAM Journal on Mathematical Finance
  28. Statistics & Decisions
  29. Stochastic Analysis and Applications
  30. Stochastic Processes and Their Applications
  31. Stochastics and Dynamics
  32. Theory of Probability and its Applications
• Technical reviewer for the IEEE CDC Proceedings (2003, 2004, 2009, 2010).
• Technical reviewer of proposals for NSERC (Canada), NRC, NSA, and NSF.
• Outside evaluator of proposals for the City University of Hong Kong (2009), K.U.Leuven (Denmark, 2009).
• NSF panel service (2006).
• Contributor to Mathematical Reviews since 1997 (83 reviews as of November 2011).

UNIVERSITY SERVICES, USC

• Associate Vise-Chair for Applied Mathematics, Fall 2005-.
• Faculty supervisor of the Putnam Mathematics Competition (2002, 2003, 2008).
• Faculty advisor and co-advisor of the undergraduate mathematics club (2002-03, Fall 2005, Fall 2006, Spring and Fall 2008, Fall 2009, Spring and Fall 2010, Spring 2011).
• Administrative committee services, Department of Mathematics
  • Member of the Department Search and Hiring Committee (2003-04).
  • Member of the Department Merit Review Committee (2001-02 and 2002-03).
  • Member of the Applied Mathematics Search and Hiring Committee (2000-01).
• Graduate exam committee services, Department of Mathematics
  • Math 555a/565a Differential Equations graduate exam: Spring and Fall 2004, Spring 2005.
  • Math 505a/507a Probability graduate exam: Fall 2002, Fall 2006, Fall 2008, Spring and Fall 2009, Fall 2010 (chair), Spring 2011 (chair), Fall 2011.
  • Math 507a/541b Probability/Statistics graduate exam: Spring 2002.
  • Math 505a/541a Probability/Statistics graduate exam: Spring 2001.
• Ph.D. oral exam committees, Department of Mathematics
  • Xuhu Wan (Fall 2003).
  • Cetin Coscun, Marios Picas, Xudong Zeng (Spring 2004).
  • Yiannis Psiloyenis, Haoyuan Liu, Huapeng Shi (Spring 2005).
  • Nilupa Sonnadara, Yangyong Zhang (Fall 2005).
  • John Mayberry (Fall 2006).
  • Youngyun Yun (Spring 2008).
  • Vlad Vicol (Fall 2008).
  • Changyong Zhang (Fall 2009).
  • Mihaela Ignatova, Jianfu Chen, Ednei Reis (Spring 2010).
  • Huanhuan Wang, Xinyang Wang (Fall 2010).
  • Shanshan Xu (Spring 2011).
  • Triet Pham, Greg Sokolov (Fall 2011).
• Ph.D. Dissertation committees
  • Yiannis Psiloyenis, Oleksandr Lytvak (Summer 2008).
  • Vlad Vicol, Changyong Zhang (Summer 2010).
• Ph.D dissertation committees, external member
  • Pansop Kim, Electrical Engineering (Fall 2003-Fall 2005).
  • Dmitriy Skvortsov, Computational Biology (Spring 2004-Fall 2005).
• Masters Thesis committees
  • Ashok Patel (Spring 2008)
• Seminars, Department of Mathematics
  • Probability and Statistics Seminar chair (2001-02).
  • Colloquium chair (2000-01).

OTHER SERVICES

• Mentor in the New Teaching Assistant program, MIT Department of Mathematics (Spring 2000).

GRADUATE STUDENTS SUPERVISED:

• Ph.D. Students
  1. (Co-Advisor with J. Cvitanic) Wei-Cheng Miao, Ph.D. in Applied Mathematics, USC. Graduation date - Spring 2004. Dissertation: Quadratic Variation Estimators for Diffusion Models in Finance. Next position: Assistant Professor, National Central University, Taiwan.
  2. Karsten Stemmann, Ph.D. in Applied Mathematics, USC. Graduation date - Summer 2006. Dissertation: Stochastic Differential Equations Driven by Colored Noise: Chaos Expansion and Application to Interest Rate Modeling. Next position: Actuary, Mercer Human Resources (Marsh and McLennan, MMC).
  3. Igor Cialenco, Ph.D. in Applied Mathematics, USC. Graduation date - Spring 2007. Dissertation: Regularity of Solution and Parameter Estimation for SPDEs with Space-Time White Noise. Next position: Assistant Professor, Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL.
  4. Xiufang Li, Ph.D. in Applied Mathematics, USC. Graduation date - Spring 2007. Dissertation: New Results on Pricing Asian Options. Next Position: Analyst, Financial Services Career Group, Chicago, IL.
  5. Qian Song, Ph.D. in Applied Mathematics, USC. Graduation date - Summer 2008. Dissertation: Optimal and Exact Control of Evolution Equations
  6. Wei Liu, Ph.D. in Applied Mathematics, USC. Graduation date - Fall 2010. Dissertation: Statistical Inference for Stochastic Hyperbolic Equations. Next position: manger of institutional credit, American Express, New York, NY.
• Master Students
  1. David Quarto, Master of Science in Applied Mathematics, USC, Department of Mathematics. Graduation date - Summer 2002. Thesis: Analysis of Wavelet Coefficients of Shifted Functions with Application to Electronic Scene Stabilization.
  2. Gloria Chen, Master of Science in Applied Mathematics, USC. Graduation date - Fall 2002. Thesis: Kernel Estimators for Stochastic Differential Equations.
  3. Chang-Hua Cheng, Master of Science in Applied Mathematics, USC. Graduation date - Spring 2003. Thesis: Stochastic Differential Equations and the Method of Sieves.
  4. Surrendra K. Markandaya, Master of Science in Applied Mathematics, USC. Graduation date - Summer 2003. Thesis: Image Stabilization Using Ridgelets.
  5. Min Xu, Master of Arts in Applied Mathematics, USC. Graduation date - Spring 2009. Thesis: Automatic Tracking of Protein Vesicles.

INVITED CONFERENCE TALKS

1. Workshop on Filtering, Center for Research in Scientific Computing, NC State University, December 1996.
2. Workshop on Stochastic Partial Differential Equations, MSRI, September 1997.
3. Conference "Stochastic Control and Filtering", USC, December 1997.
4. Workshop on Filtering, Center for Mathematical Sciences, UW Madison, July 2000.
5. Workshop "Stochastic Partial Differential Equations: Statistical Issues and Applications", University of Copenhagen, January 2001.
6. Workshop on Stochastic Partial Differential Equations, University of Warwick, UK, July 2001.
7. Twelfth International Colloquium on Differential Equations, Plovdiv Technical University, Bulgaria, August 2001.
8. Southern California Probability Symposium, UCI, November 2001.
9. International Conference "Stochastic Partial Differential Equations and Applications - VI", Levico Terme (Trento), Italy, January 2002.
10. First Joint AMS/UMI Meeting, Section "Kolmogorov Equation", Pisa, Italy, June 2002.
11. Fifteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS 2002), Section "Stochastic Control and its Applications", University of Notre Dame, August 2002.
12. Workshop on SPDEs and Related Topics, University of Warwick, UK, August 2003.
13. 4-th Southern California Applied Mathematics Symposium, Claremont, April 2004.
14. International Workshop on Nonlinear Dynamics and Stochastic Partial Differential Equations, Beijing, China, May 2004.
15. SPA (Stochastic Processes and Applications), UCSB, June 2005.
16. Conference on Differential and Difference Equations and Applications, Florida Tech., August 2005.
17. SPDE Workshop, Brown University, October 2006.
18. SAPS VI, University du Maine, March 2007.
19. SPDE workshop, Cornell University, April 2007.
20. Large Deviations Conference, University of Michigan, June 2007.
21. SPDE Workshop, Institut Mittag-Leffler, September 2007.
22. Workshop on applications of SPDEs, Institut Mittag-Leffler, November 2007.
23. International Conference "Stochastic Partial Differential Equations and Applications - VIII", Levico Terme (Trento), Italy, January 2008.
24. SIAM Annual Meeting, MS 97, July 2008.
25. SAPS VII, University du Maine, March 2009.
26. International Conference on Random Dynamical Systems, Chern Institute of Mathematics, Tianjin, China, June 2009.
27. Workshop on Stochastic Multiscale Methods, USC, August 2009.
28. AMS Meeting No. 1051, special session on SPDEs, Baylor University, Waco, TX, October 2009.
29. The 2009 Southern California Probability Symposium, UCI, December 2009.
30. Workshop on Stochastic Partial Differential Equations, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, January 2010.
31. SIAM Annual Meeting, MS 72, July 2010.
32. Workshop on Stochastic Multiscale Methods, March 2011, BIRS, Banff, Canada
33. AMS Meeting No. 1071, special session on SPDEs, University of Nevada, Las Vegas, April-May 2011.

SEMINAR TALKS

1. Probability seminar, University of Minnesota, April 1997.
2. Probability seminar, North-Eastern University, April 1998.
3. Probability and Statistics seminar, Michigan State University, June 1998.
4. PDE/Analysis seminar, MIT, April 1999.
5. Center for Mathematical Sciences seminar, University of Wisconsin, Madison, June 1999.
6. Numerical Stochastics seminar, USC, August 1999.
7. Applied Mathematics seminar, Tel-Aviv University, December 2000.
8. Probability seminar, UCI, January 2001.
9. Probability seminar, NC State University, May 2001.
10. Statistics Colloquium, UNC Chapel Hill, May 2001.
11. Statistics Colloquium, Purdue University, October 2001.
12. Analysis Seminar, USC, October 2001.
13. Probability and Stochastic Processes Seminar, Technion - Israel Institute of Technology: December 2001, December 2007.
14. Special Probability and Stochastic Processes Seminar, Technion - Israel Institute of Technology, December 2001.
15. Probability and Statistics seminar, USC: November 2002, March 2011.
16. Mathematics Colloquium, CSULB, March 2003.
17. Seminar on stochastic processes, informal session, University of Washington, March 2003.
18. Scientific Systems Company, Inc., Woburn, MA: April 2004, April 2007.
19. Finance and Stochastics Seminar, Boston University, April 2004.
20. Statistics/Probability Seminar, UC Santa Barbara, October 2004.
21. Colloquium, Department of Mathematical Sciences, WPI, January 2005.
22. Colloquium, Department of Statistics, University of Michigan, November 2005.
23. Stanford Probability Seminar, January 2007.
24. Optimization Seminar, CU Denver, January 2007.
25. Probability and Statistics Seminar, Wayne State University, February 2007.
26. Stochastic Systems Seminar, Division of Applied Mathematics, Brown University, March 2007.
27. Probability Seminar, University Paris VI, March 2007.
28. Joint Applied Mathematics/Probability Seminar, Wayne State University, June 2007.
29. The Mittag-Leffler Seminar, Institut Mittag-Leffler, September 2007.
30. Financial Mathematics Seminar, Uppsala University, November 2007.
31. Stochastics Seminar, Georgia Institute of Technology, March 2008.
32. Applied Mathematics Colloquium, Illinois Institute of Technology, March 2009.
33. Special Seminar, Huazhong University of Science and Technology, Wuhan, China, June 2009.
34. Special Lecture, South-Central University for Nationalities, Wuhan, China, June 2009.
35. Probability Seminar, Division of Applied Mathematics, Brown University: April 2010, April 2011.
36. Probability Seminar, Louisiana State University, Baton Rouge, December 2010.

EDITORIAL ACTIVITIES

1. Associate Editor, Stochastics and Dynamics, 2008-
2. V. Kaloshin, S. Lototsky, and M. Roekner, Editors. Stochastic Dynamics in Finite and Infinite Dimensions: Theory and Applications. A special issue of the journal Discrete and Continuous Dynamical Systems, Series B, Vol. 6, No. 4, July 2006.
3. P. Baxendale and S. Lototsky, Editors. Stochastic Differential Equations: Theory and Applications. A volume in honor of Professor B. L. Rozovskii. Volume 2 of the series ``Interdisciplinary Mathematical Sciences''. World Scientific, 2007.

BOOKS

1. E. K. Blum and S. V. Lototsky. Mathematics of Physics and Engineering. World Scientific, 2006. At Amazon.com
   At Barnes and Noble

PUBLICATIONS IN REFEREED JOURNALS AND VOLUMES

1. R. Sh. Liptser and S. V. Lototsky. Diffusion Approximation and Robust Kalman Filter, Journal of Mathematical Systems, Estimation and Control, Vol. 2, No. 3, pp. 263-274, 1992.
2. O. V. Gulinskii, R. Sh. Liptser, and S. V. Lototsky. Large Deviations for Unbounded Additive Functionals of Markov Processes with Discrete Time (non-compact case), Journal of Applied Mathematics and Stochastic Analysis, Vol. 7, No. 3, pp. 423-436, 1994.
3. S. V. Lototsky. Robust Algorithms of the Type of Stochastic Approximation (continuous time), Teoriya Veroyatnostei i ee Primeneninya. (Russian), Vol. 40, No. 2, pp. 324-346, 1995. English translation: Theory of Probability and its Applications (SIAM translation of the Russian journal), Vol. 40, No. 2, pp. 309-328, 1996.
4. S. V. Lototsky, C. Rao, and B. L. Rozovskii. Fast Nonlinear Filter for Continuous-Discrete Time Multiple Models, Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, Dec. 11-13, 1996, Vol. 4, pp. 4071-4076, Omnipress, Madison, WI.
5. S. V. Lototsky, R. Mikulevicius, and B. L. Rozovskii. Nonlinear Filtering Revisited: a Spectral Approach, II, Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, Dec. 11-13, 1996, Vol. 4, pp. 4060-4064, Omnipress, Madison, WI.
6. S. V. Lototsky, R. Mikulevicius, and B. L. Rozovskii. Nonlinear Filtering Revisited: a Spectral Approach , SIAM Journal on Control and Optimization, Vol. 35, No. 2, pp. 435-461, March 1997.
7. S. V. Lototsky and B. L. Rozovskii. Recursive Multiple Wiener Integral Expansion for Nonlinear Filtering of Diffusion Processes . In: J. A. Goldstein, N. E. Gretsky, and J. J. Uhl (editors), Stochastic Processes and Functional Analysis, pp. 199-208. Lecture notes in pure and applied mathematics, Vol. 186, Marcel Dekker, Inc., 1997.
8. M. Huebner, S. V. Lototsky, and B. L. Rozovskii. Asymptotic Properties of an Approximate Maximum Likelihood Estimator for Stochastic PDEs. In: Yu. M. Kabanov, B. L. Rozovskii, and A. N. Shiryaev (editors), Statistics and Control of Stochastic Processes (the Liptser festschrift), pp. 139-155. World Scientific, 1997.
9. S. V. Lototsky and B. L. Rozovskii. Recursive Nonlinear Filter for a Continuous - Discrete Time Model: Separation of Parameters and Observations, IEEE Transactions on Automatic Control, Vol. 43, No. 8, pp. 1154-1158, August 1998.
10. N. V. Krylov and S. V. Lototsky. A Sobolev Space Theory of SPDEs with Constant Coefficients on a Half Line. SIAM Journal on Mathematical Analysis. Vol. 30, No. 2, pp. 298-325, March 1999.
11. S. V. Lototsky and B. L. Rozovskii. Spectral Asymptotics of Some Functionals Arising in Statistical Inference for SPDEs. Stochastic Processes and Their Application, Vol. 79, No. 1, pp. 69-94, 1999.
12. N. V. Krylov and S. V. Lototsky. A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space. SIAM Journal on Mathematical Analysis, Vol. 31, No. 1, pp. 19-33, 2000.
13. S. V. Lototsky. Dirichlet Problem for Stochastic Parabolic Equations in Smooth Domains. Stochastics and Stochastics Reports, Vol. 68, No. 1-2, pp. 145-175, 2000.
14. M. Huebner and S. V. Lototsky. Asymptotic Analysis of the Sieve Estimator for a Class of Parabolic SPDEs. Scandinavian Journal of Statistics, Vol. 27, No. 2, pp. 353-370, 2000.
15. S. V. Lototsky and B. L. Rozovskii. Parameter Estimation for Stochastic Evolution Equations with Non-commuting Operators. In: V. Korolyuk, N. Portenko, and H. Syta (editors), Skorokhod's Ideas in Probability Theory, pp. 271-280. Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev, Ukraine, 2000.
16. S. V. Lototsky. Sobolev Spaces with Weights in Domains and Boundary Value problems for Degenerate Elliptic Equations. Methods and Applications of Analysis, Vol.7, No. 1, pp. 195-204, 2000.
17. M. Huebner and S. V. Lototsky. Asymptotic Analysis of a Kernel Estimator for Parabolic SPDEs with Time-Dependent Coefficients. Annals of Applied Probability, Vol. 10, No. 4, pp. 1-13, 2000.
18. S. V. Lototsky. Linear Stochastic Parabolic Equations, Degenerating at the Boundary. Electronic Journal of Probability, Vol. 6, paper number 24, 2001.
19. S. V. Lototsky. Small perturbation of stochastic parabolic equations: a power series analysis . Journal of Functional Analysis, Vol. 193, No. 1, pp. 94-115, 2002.
20. S. V. Lototsky. Parameter Estimation for Stochastic Parabolic Equations: Asymptotic Properties of a Two-Dimensional Projection Based Estimator. Statistical Inference for Stochastic Processes, Vol. 6, No. 1, pp. 65-87, 2003. Also available on the journal web site.
21. S. V. Lototsky. Nonlinear Filtering of Diffusion Processes in Correlated Noise: Analysis by Separation of Variables. Applied Mathematics and Optimization, Vol. 47, No. 2, pp. 167-194, 2003. Also, posted on the journal web site and the archive site.
22. S. V. Lototsky. Optimal Filtering of Stochastic Parabolic Equations. In: S. Albeverio, Z-M. Ma, and M. Roeckner (editors), Recent Developments in Stochastic Analysis and Related Topics (Proceedings of the First Sino-German Conference on Stochastic Analysis), pp. 330-353, World Scientific, 2004.
23. S. V. Lototsky and B. L. Rozovskii. Passive Scalar Equation in a Turbulent Incompressible Gaussian Velocity Field. Russian Mathematical Surveys, Vol. 59, No. 2, pp. 297-312, 2004. See also the journal web page
24. S. V. Lototsky and B. L. Rozovskii. Stochastic Differential Equations: A Wiener Chaos Approach. In: Yu. Kabanov, R. Liptser, and J. Stoyanov (editors), From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, pp. 433-507, Springer, 2006.
25. S. V. Lototsky and B. L. Rozovskii. Wiener Chaos Solutions of Linear Stochastic Evolution Equations. Annals of Probability, Vol. 34, No. 2, pp. 638-662, 2006. See also the journal web page.
26. S. V. Lototsky. Wiener Chaos and Nonlinear Filtering. Applied Mathematics and Optimization, Vol. 54, No. 3, pp. 265-291, 2006. On-line (on the official journal web page).
27. S. V. Lototsky. A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise. Communications on Stochastic Analysis, Vol. 1, No. 3, pp. 343-355, 2007.
28. S. V. Lototsky and B. L. Rozovskii. Stochastic Parabolic Equations of Full Second Order. IMA Vol. 145, pp. 199-210, 2007.
29. S. V. Lototsky and K. Stemmann. Solving SPDEs Driven by Colored Noise: a Chaos Approach. Quarterly of Applied Mathematics, Vol. 66, No. 3, pp. 499-520, 2008. Arxive Journal
30. S. V. Lototsky. Statistical Inference for Stochastic Parabolic Equations: A Spectral Approach. Publ. Mat. (Publicacions Matematiques), Vol. 53, No. 1, pp. 3–45, 2009.
31. S. V. Lototsky and K. Stemmann. Stochastic Integrals and Evolution Equations with Gaussian Random Fields. Applied Mathematics and Optimization, Vol. 59, No. 2, pp. 203-232, 2009.
32. Ig. Cialenco, S. V. Lototsky, and Jan Pospisil. Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion. Stochastics and Dynamics, Vol. 9, No. 2, pp. 169-185, 2009.
33. S. V. Lototsky and B. L. Rozovskii. Stochastic Differential Equations Driven by Purely Spatial Noise. SIAM J Math. Anal., Vol. 41, No. 4, pp. 1295-1322, 2009.
34. Ig. Cialenco and S. V. Lototsky. Parameter Estimation in Diagonalizable Bilinear Stochastic Parabolic Equations. Statistical Inference for Stochastic Processes, Vol. 12, No. 3, pp. 203-219, 2009.
35. S. V. Lototsky and B. L. Rozovskii. A Unified Approach to Stochastic Evolution Equations Using the Skorokhod Integral. Theory of Probability and its Applications, Vol. 54, No. 2, pp. 189-202, 2010.
36. W. Liu and S. V. Lototsky. Parameter Estimation in Hyperbolic Multichannel Models. Asymptotic Analysis, Vol. 68, No. 4, pp. 223-248, 2010.
37. S. V. Lototsky, B. L. Rozovskii, and X. Wan. Elliptic Equations of Higher Stochastic Order. ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM:M2AN), Volume 44, No 5, pp. 1135-1153, 2010
38. S. V. Lototsky. Chaos Approach to Nonlinear Filtering. In: D. Crisan and B. L. Rozovskii (editors), The Oxford Handbook of Nonlinear Filtering, pp. 231-264, Oxford University Press, 2011.
39. N. Lin and S. V. Lototsky. Undamped Harmonic Oscillator Driven by Additive Gaussian White Noise: A Statistical Analysis. Communications on Stochastic Analysis, Vol. 5, No. 1, pp. 233-250, 2011.
40. S. Kaligotla and S. V. Lototsky. Wick Product in The Stochastic Burgers Equation: A Curse or a Cure? Asymptotic Analysis, Vol. 75, No 3-4, pp. 145-168, 2011.

OTHER PUBLICATIONS

1. S. V. Lototsky. Problems in Statistics of Stochastic Differential Equations, Ph.D. thesis, University of Southern California, Los Angeles, CA 90089, Aug. 1996.
2. C. P. Fung and S. Lototsky. Nonlinear Filtering: Separation of Parameters and Observations Using Galerkin Approximation and Wiener Chaos Decomposition, IMA Preprint Series # 1458, February 1997.
3. S. Lototsky. Parameter Estimation for Stochastic Parabolic Equations: Asymptotic Properties of a Two-Dimensional Projection Based Estimate. IMA Preprint Series # 1486, June 1997.
4. S. V. Lototsky and B. L. Rozovskii. Time Evolution of a Passive Scalar in a Turbulent Incompressible Gaussian Velocity Field. July 2003.
5. S. V. Lototsky and K. Stemmann. From Random Processes to Generalized Fields: A Unified Approach to Stochastic Integration. October 2007.
6. W. Liu and S. V. Lototsky. Estimating Speed and Damping in the Stochastic Wave Equation. October 2008.
7. W. Liu and S. V. Lototsky. Parameter Estimation in Diagonalizable Stochastic Hyperbolic Equations. June 2009.
8. S. V. Lototsky, B. L. Rozovskii and D. Seleši A Note on Generalized Malliavin Calculus. July 2010.