Sample Solutions of Stochastic Ordinary Differential Equations

Abstract

Motivated by the stochastic differential equation x’(t,ω) = f(t, x(t,ω),ω) in Rn we prove a measurable dependence on parameters theorem for ODEs in case f is only continuous in x ε Rn. This is done by means of a known result about measurable selections of multivated maps. Afterwards we discuss consequences for stochastic ODEs. © 1985, Taylor & Francis Group, LLC. All rights reserved.