SIAM Journal on Control and Optimization, Volume 59, Issue 1, Page 434-463, January 2021.
This work is concerned with the stability, existence, and uniqueness of invariant measure for a hybrid diffusion. Under new conditions, it is shown that the hybrid diffusion possesses a unique invariant measure and its transition probability converges exponentially fast to its invariant measure under a Wasserstein distance. For the discretized process, it is demonstrated that similar results are obtained when the time step size is sufficiently small. As a result, it is shown that the invariant measure of the path-dependent hybrid diffusion can be approximated by that of the discretized process.

中文翻译：

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路径相关混合扩散分布的稳定性

SIAM控制与优化杂志，第59卷，第1期，第434-463页，2021年1月。
这项工作涉及混合扩散不变度量的稳定性，存在性和唯一性。在新的条件下，证明了混合扩散具有独特的不变性度量，并且在Wasserstein距离下其转移概率快速收敛到其不变性度量。对于离散化过程，证明了当时间步长足够小时，可以获得类似的结果。结果表明，路径依赖的混合扩散的不变性度量可以通过离散化过程的近似性来近似。