Boundedness of set-valued stochastic integrals
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2015, Vol 35, Issue 2
Abstract
The paper deals with integrable boundedness of Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4], where has not been proved that this integral is integrable bounded. The problem of integrable boundedness of the above set-valued stochastic integrals has been considered in the paper [7] and the monograph [8], but the problem has not been solved there. The first positive results dealing with this problem due to M. Michta, who showed (see [11]) that there are bounded set-valued F-nonanticipative mappings having unbounded Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim. The present paper contains some new conditions implying unboundednes of the above type set-valued stochastic integrals.
Authors and Affiliations
Michał Kisielewicz
Keywords
Related Articles
- EP ID EP469717
- DOI 10.7151/dmdico.1173
- Views 43
- Downloads 0
Pointwise strong approximation of almost periodic functions
We consider the class GM(2β) in pointwise estimate of the deviations in strong mean of almost periodic functions from matrix means of partial sums of their Fourier series.
Controllability for some Partial Functional Integrodifferential Equations with Nonlocal Conditions in Banach Spaces
This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllabilit...
Necessary conditions of optimality for a class of stochastic differential equations on UMD Banach spaces
In this paper we consider stochastic evolution equations on UMD-Banach spaces. In a recent paper we proved existence of optimal controls. Here in this paper we develop necessary conditions of optimality whereby one can...
Preface
-
A new existence results for fractional integro-differential equations of order αϵ(1,2] with nonlocal conditions in Banach spaces
In this manuscript, we examine for a class of fractional integro-differential equations (abbreviated by, FIDEs) of order αϵ(1,2] with nonlocal conditions (abbreviated by, NLCs) in Banach spaces. In the beginning, a more...