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 58
- Downloads 0
Multiple Solutions for Dirichlet Impulsive Fractional Differential Inclusions Involving the p-Laplacian with Two Parameters
In this paper, the authors establish the existence of at least three weak solutions for impulsive differential inclusions involving two parameters and the p-Laplacian and having Dirichlet boundary conditions. Their appro...
Weakly precompact operators on Cb(X,E) with the strict topology
Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(X,E) be the space of all E-valued bounded continuous functions on X, equipped with the strict topology β. We study weakly precompact operato...
Fractional Differential Inclusions of Hilfer and Hadamard Types in Banach Spaces
We deal in this paper with some existence results in Banach spaces for some Hilfer and Hadamard differential inclusions of fractional order. The Mönch's fixed point theorem and the concept of measure of noncompactness ar...
Spaces of Lipschitz functions on metric spaces
In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.
Entropy solution for doubly nonlinear elliptic anisotropic problems with Fourier boundary conditions
The goal of this paper is to study nonlinear anisotropic problems with Fourier boundary conditions. We first prove, by using the technic of monotone operators in Banach spaces, the existence of weak solutions, and by app...