论文标题
与泊松过程相关的集合随机整合的集合属性和Banach空间上相关的积分方程
Submartingale property of set-valued stochastic integration associated with Poisson process and related integral equations on Banach spaces
论文作者
论文摘要
在M型2 Banach空间中，首先，我们探讨了与固定泊松点过程相关的设定值随机积分的某些属性。通过使用HAHN分解定理和有界线性函数，我们获得了主要结果：相对于补偿泊松度量，设定值的随机过程的积分是一个固定值的sudvared substingale，但除非集成归因于单个价值的过程。其次，我们研究了设置值随机积分方程的强大解决方案，其中包括设定值的漂移，由布朗运动驱动的单值扩散以及由泊松过程驱动的设定值跳跃。
In an M-type 2 Banach space, firstly we explore some properties of the set-valued stochastic integral associated with the stationary Poisson point process. By using the Hahn decomposition theorem and bounded linear functional, we obtain the main result: the integral of a set-valued stochastic process with respect to the compensated Poisson measure is a set-valued submartingale but not a martingale unless the integrand degenerates into a single-valued process. Secondly we study the strong solution to the set-valued stochastic integral equation, which includes a set-valued drift, a single-valued diffusion driven by a Brownian motion and the set-valued jump driven by a Poisson process.
