Sample solutions of stochastic ordinary differential equations. (English) Zbl 0555.60036

Motivated by the stochastic differential equation \(x'(t,\omega)=f(t,x(t,\omega),\omega)\) in \({\mathbb{R}}^ n\) we prove a measurable dependence on parameters theorem for ODEs in case f is only continuous in \(x\in {\mathbb{R}}^ n\). This is done by means of a known result about measurable selections of multivated maps. Afterwards we discuss consequences for stochastic ODEs.


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
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