Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419350 | Journal of Mathematical Analysis and Applications | 2012 | 12 Pages |
Abstract
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 Itôʼs integrals of nonanticipative selectors of integrated set-valued processes. Immediately from Michaelʼs 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
MichaÅ Kisielewicz,