Weak compactness of weak solutions sets to stochastic differential inclusions. Issue 3 (3rd May 2020)

• Record Type: Journal Article
• Authors: Kisielewicz, Michał
• Is Part Of: Stochastic analysis and applications. Volume 38:Issue 3(2020)
• Page Start: 506
• Page End: 526
• Publication Date: 2020-05-03
• Subjects: Set-valued mappings -- set-valued stochastic integrals -- weak convergence in distribution of sequences of stochastic processes -- weak compactness in distribution of sets of stochastic processes; 60H05 -- 28B20 -- 47H04; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1702884
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: The main result of the paper deals with weak compactness in distribution of weak solutions sets to stochastic differential inclusions defined by set-valued stochastic integrals presented in the paper [Kisielewicz, M., Michta, M. (2017 ). Integrably bounded set-valued stochastic integrals. J. Math. Anal. Appl. 449(2):1892–1910]. Up to now only stochastic functional inclusions (see [Kisielewicz, M. (2013 ). Stochastic Differential and Inclusions Applications . New York: Springer]) have been investigated. The introductory parts of the paper deal with some properties of set-valued stochastic integrals and selected notions dealing with weak convergence in distribution of sequences of continuous stochastic processes.