Limit theorems for strongly and intermediately supercritical branching\n processes in random environment with linear fractional offspring\n distributions

2013/11/06 by Christian Böinghoff, Böinghoff, Christian
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60J80 #60K37 #92D25 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1311.1327

openalex publication_date 2013/11/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In the present paper, we characterize the behavior of supercritical branching\nprocesses in random environment with linear fractional offspring distributions,\nconditioned on having small, but positive values at some large generation. As\nit has been noticed in previous works, there is a phase transition in the\nbehavior of the process. Here, we examine the strongly and intermediately\nsupercritical regimes The main result is a conditional limit theorem for the\nrescaled associated random walk in the intermediately case.\n

Citations

• On Branching Processes with Random Environments: I: Extinction Probabilities
• On Branching Processes in Random Environments

Related

• Limit theorems for supercritical MBPRE with linear fractional offspring distributions
• Conditional limit theorems for intermediately subcritical branching processes in random environment
• Limit theorems for supercritical branching processes in random environment
• Simulations and a conditional limit theorem for intermediately\n subcritical branching processes in random environment
• Small positive values for supercritical branching processes in random environment