2022/11/09 by Yao Li, Li, Yao, Yaping Yuan +1
Mathematics · Physics and Astronomy · #60J28 #65C20 #92C40 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2211.04641
openalex publication_date 2022/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the sensitivity analysis of mass-action systems against their diffusion approximations, particularly the dependence on population sizes. As a continuous time Markov chain, a mass-action system can be described by a equation driven by finite many Poisson processes, which has a diffusion approximation that can be pathwisely matched. The magnitude of noise in mass-action systems is proportional to the square root of the molecule count/population, which makes a large class of mass-action systems have quasi-stationary distributions (QSDs) instead of invariant probability measures. In this paper we modify the coupling based technique developed in [8] to estimate an upper bound of the 1-Wasserstein distance between two QSDs. Some numerical results for sensitivity with different population sizes are provided.