… measures for general linear systems. We do not discuss infinite dimensional versions of
classical … We will need the following characterization of ergodic and weakly mixing systems: …

… ergodicity of the nonlinear filter. Finally, we show that our abstract results can be applied
to infinitedimensional … , stochastic spin systems and stochastic differential delay equations. …

… to ergodic behavior of solutions of stochastic partial differential equations with particular
attention paid to stochastic Navier-Stokes systems. … Next, we introduce the notion of ergodic …

0 and a potential energy term, V, which is typically the sum of pair interactions over all pairs
of particles. By thermodynamic behavior we mean, typically, that states of isolated systems …

… in [3] and by many other authors, although the present book by Da Prato and Zabczyk studies
the ergodic properties of infinite dimensional Markov processes arising as their solutions. …

… systems [10, 21, 25]. In the present paper, we are going to investigate this ergodicity question
for general infinite dimensional … from the introduced classes is weak ergodic. However, if V …

… systems of infinitely many independent particles. We will deal with one-dimensional
systems; the results and arguments can easily be adapted to several spatial dimensions. In this …

… infinite-dimensional systems. More precisely we present here some results that provide the
mathematical preliminaries to the ergodic … Thus ergodicity in this sense and equipartition are …

… The ergodic theory is basically the ergodic theory of Markov processes going back to Doob,
… have no intention of considering anything infinite dimensional. After a quick discussion of …

… The first result of this paper provides a sufficient condition for exponential ergodicity of
infinite dimensional diffusions. Let us define for each θ > 0, the triple semi-norm for f ∈ D0 as …