Set-Valued Stochastic Lebesque Integral and Representation Theorems

DOI

10.2991/ijcis.2008.1.2.8How to use a DOI?

Keywords

set-valued stochastic process, selection process, set-valued Lebesgue integral, representation

Abstract

In this paper, we shall firstly illustrate why we should introduce set-valued stochastic integrals, and then we shall discuss some properties of set-valued stochastic processes and the relation between a set-valued stochastic process and its selection set. After recalling the Aumann type definition of stochastic integral, we shall introduce a new definition of Lebesgue integral of a set-valued stochastic process with respect to the time t . Finally we shall prove the presentation theorem of set-valued stochastic integral and dis- cuss further properties that will be useful to study set-valued stochastic differential equations with their applications.

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Jungang Li
AU  - Shoumei Li
PY  - 2008
DA  - 2008/05/01
TI  - Set-Valued Stochastic Lebesque Integral and Representation Theorems
JO  - International Journal of Computational Intelligence Systems
SP  - 177
EP  - 187
VL  - 1
IS  - 2
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.2008.1.2.8
DO  - 10.2991/ijcis.2008.1.2.8
ID  - Li2008
ER  -