We formulate a criterion for the existence, uniqueness of an invariant measure for a Markov process taking values in a Polish phase space. In addition, the weak * ergodicity, that is, the weak… (More)

We deal with contracting finite and countably infinite iterated function systems acting on Polish spaces, and we introduce conformal Graph Directed Markov Systems on Polish spaces. Sufficient… (More)

This paper contains a review of results concerning “generalized” attractors for a large class of iterated function systems {wi : i∈ I} acting on a complete separable metric space. This… (More)

It is shown that every class of contracting similitudes {f1, . . . , fN} on Rs satisfying the OSC and such that dimH K0 < s, where K0 denotes the corresponding fractal, can be extended to an infinite… (More)

Generic properties of different objects (functions, sets, measures, and many others) have been studied for a long time (see [1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 15, 16]). We say that some property is… (More)

In this note we prove the law of the iterated logarithm for trajectories of particle carried by a two dimensional Eulerian velocity field. The field is given by a solution of a stochastic… (More)

It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition. 0. Introduction. Generic… (More)

We give a new criterion for the existence and statistical stability of an invariant probability measure of a Markov process taking values in a Polish phase space. The stability property in question… (More)

A new result for stability of Markov semigroups is presented. We apply this result to the equation of the passive tracer in a compressible random flow showing that the velocity of a particle… (More)