Branching random walk in random environment with random absorption wall

2018/09/13 by You Lv, Lv, You
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1809.04969

openalex publication_date 2018/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the branching random walk in random environment with a random absorption wall. When we add this barrier, we discuss some topics related to the survival probability. We assume that the random environment is i.i.d., S_i is a particular i.i.d. random walk depend on the random environment L. Let the random barrier function (the random absorption wall) is g_i(L):=ai^α-S_i, where i present the generation. We show that there exists a critical value a_c>0 such that if a>a_c,α=(1)/(3), the survival probability is positive almost surly and if a0)/n^1/3 will converges to a negative constant almost surely if α∈[0,(1)/(3)).

Citations

• Branching random walk with a random environment in time
• Brownian motion between two random trajectories

Cited by

• Small deviation for Random walk with random environment in time

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