Volume 1, Issue 2, May 2008, Pages 177 - 187
Set-Valued Stochastic Lebesque Integral and Representation Theorems
Jungang Li, Shoumei Li
Received 26 September 2007, Revised 19 December 2007, Available Online 1 May 2008.
- https://doi.org/10.2991/ijcis.2008.1.2.8How to use a DOI?
- set-valued stochastic process, selection process, set-valued Lebesgue integral, representation
- 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.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - JOUR AU - Jungang Li AU - Shoumei Li PY - 2008 DA - 2008/05 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 - https://doi.org/10.2991/ijcis.2008.1.2.8 ID - Li2008 ER -