FAST OSCILLATING RANDOM PERTURBATIONS OF DYNAMICAL-SYSTEMS WITH CONSERVATION-LAWS

被引：0

作者：

BORODIN, AN ^{[1
]}

FREIDLIN, MI ^{[1
]}

机构：

[1] RUSSIAN ACAD SCI,INST MATH,ST PETERSBURG,RUSSIA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 1995年 / 31卷 / 03期

关键词：

AVERAGING PRINCIPLE; RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS; CONSERVATION LAWS; DIFFUSION APPROXIMATION;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider fast oscillating random perturbations of dynamical systems with first integrals. We prove that if the dynamical system is ergodic in the subset of the phase space where the first integrals are constants, then the evolution of the first integrals in a proper time scale is described by a diffusion process.

引用

页码：485 / 525

页数：41

共 12 条

[1]

[Anonymous], 1984, RANDOM PERTURBATIONS

[2]

BORODIN AN, 1977, THEOR PROBAB APPL, V23, P482

[3] A STOCHASTIC-THEORY OF ADIABATIC INVARIANCE [J].

COGBURN, R ;

ELLISON, JA .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 149 (01) :97-126

[4]

DOOB JL, 1960, STOCHASTIC PROCESSES

[5]

Freidlin M., 1985, FUNCTIONAL INTEGRATI

[6] DIFFUSION-PROCESSES ON GRAPHS AND THE AVERAGING PRINCIPLE [J].

FREIDLIN, MI ;

WENTZELL, AD .

ANNALS OF PROBABILITY, 1993, 21 (04) :2215-2245

[7]

FREIDLIN MI, IN PRESS MEMOIRS AMS

[8]

Ibragimov I.A., 1978, GAUSSIAN RANDOM PROC

[9] A LIMIT THEOREM FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH RANDOM RIGHT-HAND SIDES [J].

KHASMINSKII, RZ .

THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1966, 11 (03) :390-+

[10]

KHASMINSKII RZ, 1966, THEOR PROBAB APPL+, V11, P211

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