Random walk on spheroids
Abstract:
In this talk a new technique for the path approximation of stochastic processes is presented. The results apply to the Brownian motion and to some families of stochastic differential equations whose distributions could be represented as a function of a time-changed Brownian motion (usually known as L and G-classes). I propose an explicit and easy-to-implement procedure that jointly constructs the sequences of exit times and corresponding exit positions of some well-chosen domains (the random walk on heat balls). This procedure makes it possible to approximate the first moment when Brownian motion exits a given domain, and thus to numerically solve the initial boundary value problem for the heat equation. It also makes it possible to construct a strong ε-approximation of specific one-dimensional diffusion processes. This talk is based on joint works with M. Deaconu and N. Massin.
