We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in R d with d ≤ 3.

We analyse volume-preserving actions of product groups on Riemannian manifolds. To this end, we establish a new superrigidity theorem for ergodic cocycles of product groups ranging in linear groups. There are no a priori assumptions on the acting groups, except a spectral gap assumption on their action. Our main application to manifolds concerns irreducible actions of Kazhdan product groups. We...

Abstract. We investigate uniform ergodic type theorems for additive and subadditive functions on a subshift over a finite alphabet. We show that every strictly ergodic subshift admits a uniform ergodic theorem for Banach-spacevalued additive functions. We then give a necessary and sufficient condition on a minimal subshift to allow for a uniform subadditive ergodic theorem. This provides in par...

Abstract In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on Markov–Dobrushin condition. This result generalizes estimates any positive number transition steps. An example class processes is provided to point that such considering several steps may be applicable when one can not guarantee convergence. Moreover, better obtained...

In this work, we present a new concept of measure-ergodic process to define the space measure pseudo almost periodic in p-th mean sense. We show some results regarding completeness, composition theorems and invariance consisting process. Motivated by above mentioned results, Banach fixed point theorem stochastic analysis techniques, prove existence, uniqueness global exponential stability doubl...

This paper proposes a stochastic predator–prey model with hunting cooperation and nonlinear disturbance, focuses on the effects of white noise populations. First, we present thresholds R1 R2 for extinction persistence in mean predator. When is less than 0, predator population extinct; when greater persistent mean. Moreover, by establishing suitable Lyapunov functions, investigate threshold R0 e...

For stationary ergodic diffusions satisfying nonlinear homogeneous Itô stochastic differential equations, this paper obtains the Berry–Esseen bounds on rates of convergence to normality distributions quasi maximum likelihood estimators based Taylor approximation, under some regularity conditions, when diffusion is observed at equally spaced dense time points over a long interval, high-frequency...