Random Walks and Branching Processes in Correlated Gaussian Environment

被引：3

作者：

Aurzada, Frank ^{[1
]}

Devulder, Alexis ^{[2
]}

Guillotin-Plantard, Nadine ^{[3
]}

Pene, Francoise ^{[4
,5
]}

机构：

[1] Tech Univ Darmstadt, AG Stochast, Fachbereich Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany

[2] Univ Paris Saclay, CNRS, UVSQ, Lab Math Versailles, F-78035 Versailles, France

[3] Univ Lyon 1, CNRS UMR 5208, Inst Camille Jordan, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

[4] Univ Brest, F-29238 Brest, France

[5] UMR CNRS 6205, LMBA, IUF, F-29238 Brest, France

来源：

JOURNAL OF STATISTICAL PHYSICS | 2017年 / 166卷 / 01期

关键词：

First passage time; Fractional Gaussian noise; Long-range dependence; Persistence; Random walk; Random environment; Branching process; FRACTIONAL BROWNIAN-MOTION; LIMIT-THEOREMS; PERSISTENCE; PROBABILITIES;

D O I：

10.1007/s10955-016-1677-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study persistence probabilities for random walks in correlated Gaussian random environment investigated by Oshanin et al. (Phys Rev Lett, 110:100602, 2013). From the persistence results, we can deduce properties of critical branching processes with offspring sizes geometrically distributed with correlated random parameters. More precisely, we obtain estimates on the tail distribution of its total population size, of its maximum population, and of its extinction time.

引用

页码：1 / 23

页数：23

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