Local limit approximations for Markov population processes

2009/02/05 by Sanda N. Socoll, Socoll, Sanda N., A. D. Barbour +1
Mathematics · #60J75 #62E17 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J75 #msc:62E17

paper · pdf · doi:10.48550/arxiv.0902.0886

19 pages

arxiv created 2009/02/05 · arxiv updated 2009/12/01

Abstract

The paper is concerned with the equilibrium distribution Π_n of the n-th element in a sequence of continuous-time density dependent Markov processes on the integers. Under a (2+\a)-th moment condition on the jump distributions, we establish a bound of order O(n^-(\a+1)/2√(log n)) on the difference between the point probabilities of Π_n and those of a translated Poisson distribution with the same variance. Except for the factor √(log n), the result is as good as could be obtained in the simpler setting of sums of independent integer-valued random variables. Our arguments are based on the Stein-Chen method and coupling.

Related

• Translated Poisson approximation to equilibrium distributions of Markov population processes
• Multivariate approximation in total variation, I: Equilibrium distributions of Markov jump processes
• Error bounds in local limit theorems using Stein's method
• Moment growth bounds on continuous time Markov processes on non-negative integer lattices
• Stein's method and locally dependent point process approximation