Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar by Igor Cialenco: A Power Variation Approach to Statistical Analysis of Discretely Sampled Semilinear SPDEs

Speaker: Igor Cialenco, Illinois Institute of Technology

Title:  A power variation approach to statistical analysis of discretely sampled semilinear SPDEs

Abstract:  Motivated by problems from statistical analysis for discretely sampled SPDEs, we derive central limit theorems for higher order finite differences applied to stochastic processes with arbitrary finitely regular paths. We prove a new central limit theorem for some power variations of the iterated integrals of a fractional Brownian motion (fBm) and consequently apply them to estimation of the drift and volatility coefficients of semilinear stochastic partial differential equations driven by an additive Gaussian noise white in time and possibly colored in space. In particular, we show that approximating naively derivatives by finite differences in certain estimators may introduce a nontrivial bias that we compute explicitly. The talk should be accessible to all graduate students and undergraduate students with background in probability and statistics.

 

Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar