Homotopy Continuation Methods for Stochastic Two-Point Boundary Value Problems Driven by Additive Noises

Abstract

In this paper the homotopy continuation method for stochastic two-point boundary value problems driven by additive noises is studied. The existence of the solution of the homotopy equation is proved. Numerical schemes are constructed and error estimates are obtained. Numerical experiments demonstrate the effectiveness of the homotopy continuation method over other commonly used methods such as the shooting method.