2023/07/02 by Wuchen Li, Li, Wuchen
Computer Science · Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Control (math.OC) #Probability (math.PR) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2307.00678
openalex publication_date 2023/07/02 · openalex created_date 2023/07/06 · openalex updated_date 2026/07/28
We study gradient drift-diffusion processes on a probability simplex set with finite state Wasserstein metrics, namely finite state Wasserstein common noises. A fact is that the Kolmogorov transition equation of finite reversible Markov processes satisfies the gradient flow of entropy in finite state Wasserstein space. This paper proposes to perturb finite state Markov processes with Wasserstein common noises. In this way, we introduce a class of stochastic reversible Markov processes. We also define stochastic transition rate matrices, namely Wasserstein Q-matrices, for the proposed stochastic Markov processes. We then derive the functional Fokker-Planck equation in the probability simplex, whose stationary distribution is a Gibbs distribution of entropy functional in a simplex set. Several examples of Wasserstein drift-diffusion processes on a two-point state space are presented.