Volume 2, Issue 1, March 2009, Pages 83 - 90
Aumann Type Set-valued Lebesgue Integral and Representation Theorem
- Jungang Li, Shoumei Li
Available Online 1 April 2009.
- https://doi.org/10.2991/jnmp.2009.2.1.9How to use a DOI?
- 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.
- Open Access
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Cite this article
TY - JOUR AU - Jungang Li AU - Shoumei Li PY - 2009 DA - 2009/04 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 - https://doi.org/10.2991/jnmp.2009.2.1.9 ID - Li2009 ER -