First Exit Times of Non-linear Dynamical Systems in Rd Perturbed by Multifractal Levy Noise

被引：9

作者：

Imkeller, Peter ^{[2
]}

Pavlyukevich, Ilya ^{[1
]}

Stauch, Michael ^{[2
]}

机构：

[1] Univ Jena, Inst Stochast, D-07743 Jena, Germany

[2] Humboldt Univ, Inst Math, D-12489 Berlin, Germany

来源：

JOURNAL OF STATISTICAL PHYSICS | 2010年 / 141卷 / 01期

关键词：

Levy process; Levy flight; First exit time; Exit time law; Perturbed dynamical system; Multifractal noise; DRIVEN; FORCE;

D O I：

10.1007/s10955-010-0041-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In a domain G subset of R-d we study a dynamical system which is perturbed in finitely many directions i by one-dimensional Levy processes with alpha (i) -stable components. We investigate the exit behavior of the system from the domain in the small noise limit. Using probabilistic estimates on the Laplace transform of the exit time we show that it is exponentially distributed with a parameter that depends on the smallest alpha (i) . Finally we prove that the system exits from the domain in the direction of the process with the smallest alpha (i) .

引用

页码：94 / 119

页数：26

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