INVARIANT MEASURES OF STOCHASTIC PERTURBATIONS OF DYNAMICAL SYSTEMS USING FOURIER APPROXIMATIONS

被引：3
|
作者：
Islam, Md Shafiqul [1 ]
Gora, Pawel [2 ]
机构：
[1] Univ Prince Edward Isl, Dept Math & Stat, Charlottetown, PE C1A 4P3, Canada
[2] Concordia Univ, Dept Math & Stat, Montreal, PQ H4B 1R6, Canada
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2011年 / 21卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Stochastic perturbations of dynamical systems; Fourier approximation; Frobenius-Perron operator; probability density function; absolutely continuous invariant measures; MAPS;
D O I：
10.1142/S0218127411028283
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider dynamical system tau : [0, 1] -> [0, 1] and its stochastic perturbations (q) over bar (N)(tau(x), .), N >= 1. Using Fourier approximation, we construct a finite dimensional approximation P(N) to a perturbed Perron-Frobenius operator. Let (f) over cap be an invariant density of tau and f(N)* be a fixed point of P(N). We show that {f(N)*} converges in L(1) to (f) over cap.
引用
收藏
页码：113 / 123
页数：11
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