Office Hours: MW 9:30-10am and 12-12:30pm, in KAP 245
Walk-ins and appointments at other time are welcome.
Course objective To learn about current research in the area of statistics for SPDEs. While at that, we will review and/or learn a number of interesting and useful topics in statistics and stochastic analysis.
Course work Class participation, homework assignments, final presentation
Official grading scheme 20% class participation, 40% homework assignments, 40% final presentation.
Main reference S. V. Lototsky. Statistical Inference for Stochastic Parabolic Equations: A Spectral Approach. Publ. Mat. (Publicacions Matematiques), Vol. 53, No. 1, pp. 3–45, 2009.
May 16. The big picture and the stochastic heat equation on the interval.
May 21. Stochastic heat equation on the interval: definition and construction of solution.
May 23. Stochastic heat equation on the interval: derivation and properties of the MLE of the diffusion coefficient.
May 30. General parabolic equation and the order condition.
June 4. Two general ideas: regular statistical experiment and elliptic operators. The first set of individual problems is due.
June 6. Discussion session on group problems
June 11. Examples; observations in discrete time; some non-commuting cases.
June 13. Hyperbolic model
June 18. Multiplicative time-only noise
June 20. Time-dependent coefficient: methods of sieves and kernel estimator
June 25. Summary. The second set of individual problems is due.
June 27. Discussion session on potential research problems.
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