Inserted: 22 jun 2010
Last Updated: 18 jan 2015
Journal: St. Petersburg Math. J
We prove the existence of an invariant measure for (families of) generalized weighted shifts, which we call ``atomic operators''. Typically, such operators may come from infinite dimensional stochastic differential equations generating non-Carathéodory stochastic flows, for instance, from stochastic differential equation with time delay in the diffusion. The main result is applied then to such flows giving the existence of invariant measures for those.
Keywords: Young Measures, shift operator, local operator, random dynamical system, invariant measure, cocycle property, Wiener shift