Set-Valued Square Integrable Martingales and Stochastic Integral

摘要

In this paper, we firstly introduce the concept of set-valued square integrable martingales. Secondly, we give the definition of stochastic integral of a stochastic process with respect to a set-valued square integrable martingale, and then prove the representation theorem of this kind of integral processes. Finally, we show that the stochastic integral process is a set-valued sub-martingale.