Statistical analysis of SPDEs – exploring singularities

12.01.2024, 10:15 - 11:15  –

Igor Cialenco, Illinois Institute of Technology

Unlike traditional finite-dimensional stochastic differential equations, statistical models driven by SPDEs are predominantly singular, when the solution is observed on a finite time interval. Hence, conventional inference tools are inadequate and special methods must be developed. After a brief discussion of some classical approaches, we will discuss some classes of parabolic SPDEs for which exploring some specific structures yield intriguing results or unexpected anomalies, e.g. finding parameters bypassing statistical procedures, or introducing nontrivial biases after naïve approximations of estimators. We continue by exploring some cutting-edge methodologies in estimating some of the parameters entering (nonlinear) SPDEs, and conclude with some open problems and possible research directions.   

Introducing "What is...?" lecture for young scientists from 9:15 to 10 am in room 1.22, building 9.

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