Set-valued stochastic integral equations driven by martingales

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• 作者：Marek T. Malinowski^a ; ^{m.malinowski@wmie.uz.zgora.pl} ; Mariusz Michta^a ; ^b ; ^{m.michta@wmie.uz.zgora.pl}
• 关键词：Set-valued and fuzzy stochastic Lebesgue&ndash ; Stieltjes trajectory integral ; Set-valued and fuzzy stochastic trajectory integral with respect to martingale ; Set-valued and fuzzy stochastic integral equation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：1 October, 2012
• 卷：394
• 期：1
• 页码：30-47
• 文件大小：308 K

摘要

We consider a notion of set-valued stochastic Lebesgue-Stieltjes trajectory integral and a notion of set-valued stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of set-valued stochastic integral equations. The existence and uniqueness of the solution to such the equations is proven. As a generalization of set-valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales.