FROM THE PERRON-FROBENIUS EQUATION TO THE FOKKER-PLANCK EQUATION

被引：28

作者：

BECK, C ^{[1
]}

机构：

[1] UNIV LONDON,QUEEN MARY & WESTFIELD COLL,SCH MATH SCI,LONDON E1 4NS,ENGLAND

来源：

JOURNAL OF STATISTICAL PHYSICS | 1995年 / 79卷 / 5-6期

关键词：

PERRON-FROBENIUS EQUATION; FOKKER-PLANCK EQUATION; SCALING LIMITS; MAPS OF KAPLAN-YORKE TYPE; CORRECTIONS TO GAUSSIAN BEHAVIOR; OMEGA-EXPANSION;

D O I：

10.1007/BF02181207

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show that for certain classes of deterministic dynamical systems the Perron-Frobenius equation reduces to the Fokker-Planck equation in an appropriate scaling limit. By perturbative expansion in a small time scale parameter, we also derive the equations that are obeyed by the first- and second-order correction terms to the Fokker-Planck limit case. In general, these equations describe non-Gaussian corrections to a Langevin dynamics due to an underlying deterministic chaotic dynamics. For double-symmetric maps, the first-order correction term turns out to satisfy a kind of inhomogeneous Fokker-Planck equation with a source term. For a special example, we are able solve the first-and second-order equations explicitly.

引用

页码：875 / 894

页数：20

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