On connections between stochastic differential inclusions and set-valued stochastic differential equations driven by semimartingales

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• 作者：Mariusz Michta ^{m.michta@wmie.uz.zgora.pl}
• 关键词：Set-valued function ; Stochastic differential inclusion ; Set-valued stochastic differential equation ; Semimartingale ; Attainable set ; Continuous selection
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：2106-2134
• 全文大小：413 K
• 卷排序：262

文摘

In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations with respect to semimartingale integrators. We present new connections between their solutions. In particular, we show that attainable sets of solutions to stochastic inclusions are subsets of values of multivalued solutions of certain set-valued stochastic equations. We also show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. The results obtained in the paper generalize results dealing with this topic known both in deterministic and stochastic cases.