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On exponential convergence to a stationary measure for a class of random dynamical systems

Sergei B. Kuksin (2001)

Journées équations aux dérivées partielles

For a class of random dynamical systems which describe dissipative nonlinear PDEs perturbed by a bounded random kick-force, I propose a “direct proof” of the uniqueness of the stationary measure and exponential convergence of solutions to this measure, by showing that the transfer-operator, acting in the space of probability measures given the Kantorovich metric, defines a contraction of this space.

Smooth Extensions of Bernoulli Shifts

Zbigniew S. Kowalski (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

For homographic extensions of the one-sided Bernoulli shift we construct σ-finite invariant and ergodic product measures. We apply the above to the description of invariant product probability measures for smooth extensions of one-sided Bernoulli shifts.

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