论文标题
由相对赛车驱动的随机微分方程
Stochastic differential equations driven by relative martingales
论文作者
论文摘要
本文有助于对相对群众的研究。具体来说，对于封闭的随机套件$ h $，它们在$ h $上为$ h $的过程无效，将$ m = m+v $分解为$ m $，其中$ m $是càdlàg均匀整合的martingale，$ v $是一个连续的过程，具有可集成的变化，因此$ v_ {0} = 0} = 0} = 0 $ $ dv $ caus $ h $ a $ h $。首先，我们将此概念扩展到随机流程，不一定在$ h $上无效，其中$ m $被认为是本地的martingale而不是统一的可整合的玛特宁格。因此，我们通过呈现一些结构特性，为新的较大类相对群的一般框架提供了一个一般框架。其次，作为应用程序，我们使用上述新类的连续随机过程构建了偏度布朗运动方程的解决方案。此外，我们研究了由相对martingale驱动的随机微分方程。
This paper contributes to the study of relative martingales. Specifically, for a closed random set $H$, they are processes null on $H$ which decompose as $M=m+v$, where $m$ is a càdlàg uniformly integrable martingale and, $v$ is a continuous process with integrable variations such that $v_{0}=0$ and $dv$ is carried by $H$. First, we extend this notion to stochastic processes not necessarily null on $H$, where $m$ is considered local martingale instead of a uniformly integrable martingale. Thus, we provide a general framework for the new larger class of relative martingales by presenting some structural properties. Second, as applications, we construct solutions for skew Brownian motion equations using continuous stochastic processes of the above mentioned new class. In addition, we investigate stochastic differential equations driven by a relative martingale.
