马尔科夫链驱动的带停时的超前倒向随机微分方程的适应解

Adapted Solutions of Anticipated Backward Stochastic Differential Equations with Stopping Time on Markov Chain

考虑有限随机区间上由马尔科夫链驱动的超前倒向随机微分方程。假设由马尔科夫链驱动的带停时的超前倒向随机微分方程的生成元满足Lipschitz条件,通过Doob鞅不等式以及不动点定理,证明由马尔科夫过程驱动的有限随机区间上的超前倒向随机微分方程存在唯一解。

The paper studies the anticipated backward stochastic differential equation on the Markov chain on a finite random interval.Assuming that the generator of the anticipated backward stochastic differential equation with stopping time on the Markov chain satisfies the Lipschitz condition,and employing through Doob's martingale inequality and the fixed point theorem,we can prove that there is a unique adapted solution to the anticipated backward stochastic differential equation with stopping time on the Markov chain.