Deterministic representation for position dependent random maps

被引：0

作者：

Bahsoun, Wael ^{[2
]}

Bose, Christopher ^{[1
]}

Quas, Anthony ^{[1
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[2] Univ Manchester, Manchester M13 9PL, Lancs, England

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2008年 / 22卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

random map; skew product; absolutely continuous invariant measure;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a deterministic representation for position dependent random maps and describe the structure of its set of invariant measures. Our construction generalizes the skew product representation of random maps with constant probabilities. In particular, we establish one-to-one correspondence between eigenfunctions corresponding to eigenvalues of unit modulus for the Frobenius-Perron (transfer) operator of the random map and for those of the skew. An immediate consequence is one-to-one correspondence between absolutely continuous invariant measures (acims) for the position dependent random map and acims for its deterministic representation.

引用

页码：529 / 540

页数：12

共 7 条

[1]

Arnold L., 1998, SPRINGER MONOGRAPHS

[2] Absolutely continuous invariant measures for random maps with position dependent probabilities [J].