16 research outputs found
Passive tracer in a flow corresponding to a two dimensional stochastic Navier Stokes equations
In this paper we prove the law of large numbers and central limit theorem for
trajectories of a particle carried by a two dimensional Eulerian velocity
field. The field is given by a solution of a stochastic Navier--Stokes system
with a non-degenerate noise. The spectral gap property, with respect to
Wasserstein metric, for such a system has been shown in [9]. In the present
paper we show that a similar property holds for the environment process
corresponding to the Lagrangian observations of the velocity. In consequence we
conclude the law of large numbers and the central limit theorem for the tracer.
The proof of the central limit theorem relies on the martingale approximation
of the trajectory process
On a Unique Ergodicity of Some Markov Processes
It is proved that the sufficient condition for the uniqueness of an invariant
measure for Markov processes with the strong asymptotic Feller property formulated
by Hairer and Mattingly (Ann Math 164(3):993–1032, 2006) entails the existence of
at most one invariant measure for e-processes as well. Some application to timehomogeneous
Markov processes associated with a nonlinear heat equation driven by
an impulsive noise is also given
The Central Limit Theorem for Random Dynamical Systems
We consider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. The Central Limit Theorem for random dynamical systems is established