On a new set-valued stochastic integral with respect to semimartingales and its applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:408

Article

Malinowski, Marek T.

关键词: Set-valued stochastic integrals;    Stochastic differential inclusion;    Set-valued stochastic integral equation;    Existence of solution;    Semimartingale;    Fuzzy stochastic integral;    Fuzzy stochastic differential equation;   

DOI  :  10.1016/j.jmaa.2013.06.054

来源: Elsevier

【 摘 要 】

We present a new approach to a concept of a set-valued stochastic integral with respect to semi martingales. Such an integral, called set-valued stochastic up-trajectory integral, is compatible with the decomposition of the semimartingale. Some properties of this integral are stated. We show applicability of the new integral in set-valued stochastic integral equations driven by multidimensional semimartingales. The uniqueness theorem is presented. Then we extend the notion of the set-valued stochastic up-trajectory integral to definition of a fuzzy stochastic up-trajectory integral with respect to semimartingales. A result on uniqueness of a solution to fuzzy stochastic integral equations incorporating the new fuzzy stochastic up-trajectory integral driven by the multidimensional semimartingale is stated. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free