Stochastic dynamical systems with weak contractivity properties I. Strong and local contractivity

Marc Peigné, and Wolfgang Woess. "Stochastic dynamical systems with weak contractivity properties I. Strong and local contractivity." Colloquium Mathematicae 125.1 (2011): 31-54. <http://eudml.org/doc/283524>.

@article{MarcPeigné2011,
abstract = {Consider a proper metric space and a sequence $(Fₙ)_\{n≥0\}$ of i.i.d. random continuous mappings → . It induces the stochastic dynamical system (SDS) $Xₙ^\{x\} = Fₙ ∘ ... ∘ F₁(x)$ starting at x ∈ . In this and the subsequent paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process. In the present first part, we elaborate, improve and complete the unpublished work of Martin Benda on local contractivity, which merits publicity and provides an important tool for studying stochastic iterations. We consider the case when the Fₙ are contractions and, in particular, discuss recurrence criteria and their sharpness for the reflected random walk.},
author = {Marc Peigné, Wolfgang Woess},
journal = {Colloquium Mathematicae},
keywords = {stochastic iterated function system; local contractivity; recurrence; invariant measure; ergodicity; affine stochastic recursion; reflected random walk},
language = {eng},
number = {1},
pages = {31-54},
title = {Stochastic dynamical systems with weak contractivity properties I. Strong and local contractivity},
url = {http://eudml.org/doc/283524},
volume = {125},
year = {2011},
}

TY - JOUR
AU - Marc Peigné
AU - Wolfgang Woess
TI - Stochastic dynamical systems with weak contractivity properties I. Strong and local contractivity
JO - Colloquium Mathematicae
PY - 2011
VL - 125
IS - 1
SP - 31
EP - 54
AB - Consider a proper metric space and a sequence $(Fₙ)_{n≥0}$ of i.i.d. random continuous mappings → . It induces the stochastic dynamical system (SDS) $Xₙ^{x} = Fₙ ∘ ... ∘ F₁(x)$ starting at x ∈ . In this and the subsequent paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process. In the present first part, we elaborate, improve and complete the unpublished work of Martin Benda on local contractivity, which merits publicity and provides an important tool for studying stochastic iterations. We consider the case when the Fₙ are contractions and, in particular, discuss recurrence criteria and their sharpness for the reflected random walk.
LA - eng
KW - stochastic iterated function system; local contractivity; recurrence; invariant measure; ergodicity; affine stochastic recursion; reflected random walk
UR - http://eudml.org/doc/283524
ER -