B0592
Title: A power variation approach to statistical analysis of discretely sampled semilinear SPDEs
Authors: Igor Cialenco - Illinois Institute of Technology (United States) [presenting]
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 the 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.
