Aumann Type Set-valued Lebesgue Integral and Representation Theorem

作者：Li Jungang^*; Li Shoumei

来源：International Journal of Computational Intelligence Systems, 2009, 2(1): 83-90.

DOI：10.2991/jnmp.2009.2.1.9

• set-valued stochastic process
• set-valued Lebesgue integral
• Aumann type integral
• representation theorem

In 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.

• 出版日期2009-3
• 单位北京工业大学