Statistical inference for the stochastic heat equation

Abstract

This thesis is concerned with two p-variation type estimators for the parameters _ (diffusivity) and _2 (noise size) of the stochastic heat equation, proposed by Cialenco and Huang [3]. The theory of the stochastic heat equation is reviewed. The theory of pvariation type estimators is reviewed and p-variation type estimators relating to the stochastic heat equation are introduced. These estimators are investigated numerically. From the simulation results, it is conjectured that the estimators for _ as well as the estimators for _2 converge in mean and root mean square with convergence rate 1/2