Aumann Type Set-valued Lebesgue Integral and Representation Theorem

DOI

10.2991/jnmp.2009.2.1.9How to use a DOI?

Abstract

n this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact subset of d -dimensional Euclidean space. After recalling some basic results about set-valued stochastic processes, we shall secondly prove that the Aumann type set-valued Lebesgue integral of a set-valued stochastic process above is a set-valued stochastic process. Finally we shall give the representation theorem, and prove an important inequality of the Aumann type set-valued Lebesgue integrals of set-valued stochastic processes with respect to t , which are useful to study set-valued stochastic differential inclusions with applications in finance.

Copyright

© 2009, 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  - 2009
DA  - 2009/03/01
TI  - Aumann Type Set-valued Lebesgue Integral and Representation Theorem
JO  - International Journal of Computational Intelligence Systems
SP  - 83
EP  - 90
VL  - 2
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/jnmp.2009.2.1.9
DO  - 10.2991/jnmp.2009.2.1.9
ID  - Li2009
ER  -