Tomasz Komorowski

On ergodicity of some Markov processes

We formulate a criterion for the existence and uniqueness of an invariant measure for a Markov process taking values in a Polish phase space. In addition, weak- * ergodicity, that is, the weak convergence of the ergodic averages of the laws of the process starting from any initial distribution, is established. The principal assumptions are the existence of a lower bound for the ergodic averages of the transition probability function and its local uniform continuity. The latter is called the e-property. The general result is applied to solutions of some stochastic evolution equations in Hilbert spaces. As an example, we consider an evolution equation whose solution describes the Lagrangian observations of the velocity field in the passive tracer model. The weak- * mean ergodicity of the corresponding invariant measure is used to derive the law of large numbers for the trajectory of a tracer.

LIMIT THEOREMS FOR ADDITIVE FUNCTIONALS OF A MARKOV CHAIN

Consider a Markov chain

On homogenization of time-dependent random flows

{X_n}_{nge 0}

Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise

with an ergodic probability measure

Diffusion in a Weakly Random Hamiltonian Flow

pi

Lagrangian dynamics for a passive tracer in a class of Gaussian Markovian flows

. Let

On the sector condition and homogenization of diffusions with a Gaussian drift

Psi

On the Superdiffusive Behavior of Passive Tracer with a Gaussian Drift

a function on the state space of the chain, with

Diffusive and Nondiffusive Limits of Transport in Nonmixing Flows

alpha

Passive tracer in a slowly decorrelating random flow with a large mean

-tails with respect to