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Stochastic differential inclusions. (English) Zbl 0979.93109

The author defines a new notion of solution for stochastic differential inclusions of the form \[ dZ_t\in F(Z_t) dX_t, \] where \(F\) and \(X\) are given stochastic processes.
When \(F\) is convex valued, bounded and Lipschitz continuous and when \(X\) is an \(H^\infty\)-bounded convex set valued semimartingale, then the above stochastic differential inclusion admits at least one solution.

MSC:

93E03 Stochastic systems in control theory (general)
34A60 Ordinary differential inclusions
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