分数Brown运动驱动带Markov切换的随机微分方程解的密度存在性

The existence of the density for the solution of stochastic differential equation driven by fractional Brownian motion with Markovian switching

本文研究分数Brown运动驱动带Markov切换的随机微分方程,获得了方程解的存在唯一性,定义了关于解的条件Malliavin分析,在扩散系数非退化的条件下,证明了解的Malliavin正则性,从而得到了解分布关于Lebesgue测度绝对连续.

This paper studies the solution of stochastic differential equation driven by fractional Brownian motion with Markovian switching. We get the existence and uniqueness for the solution. The conditional Malliavin calculus is defined. And the Malliavin regularity of the solution is obtained under the nondegenerate condition of the diffusion coefficient. This yields that the law of the solution is absolute continuity with respect to the Lebesgue measure.