Central Limit Theorems for Supercritical Branching Markov Processes

2013/05/03 by Yu‐Xin Ren, Renming Song, Ren, Y. -X. +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1305.0610

openalex publication_date 2013/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems proved in [1], P. for branching OU processes with binary branching mechanisms. Compared with the results of [1], our central limit theorems are more satisfactory in the sense that the normal random variables in our theorems are non-degenerate.

Cited by

• A moment approach to the law of large numbers for supercritical branching Markov processes
• Law of iterated logarithm for supercritical non-symmetric branching Markov process

Related

• Central Limit Theorems for Supercritical Branching Nonsymmetric Markov Processes
• Central limit theorems for branching processes under mild assumptions on the mean semigroup
• Functional central limit theorems for supercritical superprocesses
• Central Limit Theorems for Supercritical Superprocesses
• Central Limit Theorems for Super-OU Processes