Calculus of Variations and Geometric Measure Theory

A. Ponosov - E. Stepanov

Invariant measures for generalized random dynamical systems

created on 23 Nov 2003
modified by stepanov on 15 Oct 2006


Published Paper

Inserted: 23 nov 2003
Last Updated: 15 oct 2006

Journal: International conference on fixed point theory and its applications (Valencia, 2003), G.G. Falset, E.L Fuster, B. Sims (ed.), Yokohama publishers, Yokohama
Pages: 227-260
Year: 2004


The results proved in this paper provide existence of an invariant measure for non-Carathéodory random dynamical systems typically coming from stochastic differential equations with nonregular solution flows. An example of such an equation is a stochastic differential equation with time delay in the diffusion.

Keywords: local operator, atomic operator, random dynamical system, invariant measure, stochastic flow, strong periodic solutions, stationary solutions, stochastic delay equation