On the Fundamental Theory of Nonlinear Second Order Stochastic Boundary Value Problems

Abstract

**Please note that the full text is embargoed** ABSTRACT: A Study of nonlinear second order stochastic boundary value problems (SBVP for short) is initiated through sample calculus approach. A basic existence result for bounded nonlinearities is established. The method of upper and lower solution processes and a general existence theorem are established. After proving the stochastic version of the needed maximum principle, the monotone iterative technique is developed which yields existence of multiple solution processes of SBVP. Finally, by developing a stochastic comparison result, the important problem of finding error estimates between the sample solutions of SBVP and the solutions of corresponding mean BVP, is considered.