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On the stability properties by quasi-expectation of stochastic set solutions with selectors. (English) Zbl 1239.60048

The authors are interested in generating the stochastic set of processes \(X_t=X(t,\omega)\in K_{cc}(\mathbb{R}^n)\), where \(t\in[0,\tau]\subset\mathbb{R}_+\) and \(K_{cc}(\mathbb{R}^n)\) are the family of all nonempty convex and compact subsets of the Euclidian \(n\)-dimensional space \(\mathbb{R}^n\) with Hausdorff distance. They investigate stability properties by quasi-expectation of stochastic set solutions for stochastic set differential equations under Hukuhara derivative with selectors without any controls.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34G10 Linear differential equations in abstract spaces
47D06 One-parameter semigroups and linear evolution equations
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