Some properties of set-valued stochastic integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Kisielewicz, Michal

关键词: Set-valued mappings;    Set-valued integrals;    Set-valued stochastic processes;   

DOI  :  10.1016/j.jmaa.2011.10.050

来源: Elsevier

【 摘 要 】

The present paper is devoted to properties of set-valued stochastic integrals defined as some special type of set-valued random variables. In particular, it is shown that if the probability base is separable or probability measure is nonatomic then defined set-valued stochastic integrals can be represented by a sequence of Ito's integrals of nonanticipative selectors of integrated set-valued processes. Immediately from Michael's continuous selection theorem it follows that the indefinite set-valued stochastic integrals possess some continuous selections. The problem of integrably boundedness of set-valued stochastic integrals is considered. Some remarks dealing with stochastic differential inclusions are also given. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free