Now in its second edition, this book gives a systematic and self-contained presentation of
basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and …

The general topic of this book is the ergodic behavior of Markov processes. A detailed
introduction to methods for proving ergodicity and upper bounds for ergodic rates is …

We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential
equations with general multiplicative noise within the framework of kinetic solutions. Our …

Suppose that {Xt, t≥ 0} is a non-stationary Markov process, taking values in a Polish metric
space E. We prove the law of large numbers and central limit theorem for an additive …

We illustrate how the notion of asymptotic coupling provides a flexible and intuitive
framework for proving the uniqueness of invariant measures for a variety of stochastic partial …

The Markov chain model is widely applied in many fields, especially the field of prediction.
The discrete-time Markov chain (DTMC) is a common method for prediction. However, the …

摘要马尔科夫链以其无后效性广泛应用于自然科学和工程技术领域. 经典的马尔科夫链并不能
反映对象状态的不确定性, 并且当状态划分边界过于清晰时, 状态转移情况不稳定 …

We provide sufficient conditions for the uniqueness of an invariant measure of a Markov
process as well as for the weak convergence of transition probabilities to the invariant …

We establish the exponential convergence with respect to the L 1-Wasserstein distance and
the total variation for the semigroup corresponding to the stochastic differential equation d X …

The ergodicity of SDEs and SPDEs, in which the state spaces are independent of the past,
has been studied extensively. So far, there are several approaches to investigate ergodicity …