On the structure of attractors and invariant measures for a class of monotone random systems

Authors: Chueshov I.¹; Scheutzow M.²

Source: Dynamical Systems: An International Journal, Volume 19, Number 2, June 2004 , pp. 127-144(18)

Buy & download fulltext article:

Price: $56.94 plus tax (Refund Policy)

Abstract:

Under rather general conditions we show that any monotone random dynamical system on an (admissible) subset of a partially ordered Banach space V has a unique invariant measure. This measure is Dirac, i.e. it is generated by some stationary process. If the cone V₊ of non-negative elements of V is normal, then this stationary process is a global random attractor with respect to convergence in probability. As examples we consider one-dimensional ordinary and retarded stochastic differential equations, a stochastic model of a biochemical control circuit, a class of parabolic stochastic partial differential equations (PDEs) with additive noise and interacting particle systems.

Document Type: Research article

DOI: http://dx.doi.org/10.1080/1468936042000207792

Affiliations: 1: Department of Mechanics and Mathematics Kharkov University 61077 Kharkov Ukraine, Email: chueshov@univer.kharkov.ua 2: Institut für Mathematik Sekr. MA 7-5 Fakultät II-Mathematik and Naturwissenschaften Technische Universität Berlin Str. des 17 Juni 136 10623 Berlin Germany, Email: ms@math.tu-berlin.de

Publication date: 2004-06-01

More about this publication?