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

Deimling, K.

Stochastic Anal. Appl. 3, 15-21 (1985).

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.

MSC:

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

Keywords:

measurable dependence on parameters theorem; measurable selections

References:

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