Time-dependent weak rate of convergence for functions of generalized bounded variation

Abstract

Let W denote the Brownian motion. For any exponentially bounded Borel function g the function u defined by is the stochastic solution of the backward heat equation with terminal condition g. Let denote the corresponding approximation generated by a simple symmetric random walk with time steps and space steps where For a class of terminal functions g having bounded variation on compact intervals, the rate of convergence of to u(t, x) is considered, and also the behavior of the error as t tends to T.