相关论文: On some results on the stability of Markov operato…

The relations between asymptotic stability, the eventual e-property and the e-property of Markov semigroups, acting on measures defined on general (Polish) metric spaces, are studied. While usually much attention is paid to asymptotic…

In this paper, we establish three criteria for the asymptotic behavior of Markov-Feller semigroups. First, we present a criterion for convergence in total variation to a unique invariant measure, requiring only $TV$-eventual continuity of…

Let $U\subset K$ be an open and dense subset of a compact metric space and let $\{\Phi_t\}_{t\ge0}$ be a Markov semigroup on the space of bounded Borel measurable functions on $U$ with the strong Feller property. Suppose that for each…

For an increasing sequence $(T_n)$ of one-parameter semigroups of sub Markovian kernel operators over a Polish space, we study the limit semigroup and prove sufficient conditions for it to be strongly Feller. In particular, we show that the…

Relation between equicontinuity, the so called e property and stability of Markov operators is studied. In particular, it is shown that any asymptotically stable Markov operator with an invariant measure such that the interior of its…

In this work, we prove that any asymptotically stable Markov-Feller operator possesses the e-property everywhere outside at most a meagre set. We also provide an example showing that this result is tight. Moreover, an equivalent criterion…

We give a new, two-step approach to prove existence of finite invariant measures for a given Markovian semigroup. First, we identify a convenient auxiliary measure and then we prove conditions equivalent to the existence of an invariant…

In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equations with unbounded coefficients. We prove that these…

We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply…

We formulate a new criterion of the asymptotic stability for some non-equicontinuous Markov semigroups, the so-called eventually continuous semigroups. In particular, we provide a non-equicontinuous Markov semigroup example with essential…

This paper investigates the ergodicity of Markov--Feller semigroups on Polish spaces, focusing on very weak regularity conditions, particularly the Ces\`aro eventual continuity. First, it is showed that the Ces\`aro average of such…

The existence of Feller semigroups arising in the theory of multidimensional diffusion processes is studied. An elliptic operator of second order is considered on a plane bounded region $G$. Its domain of definition consists of continuous…

We consider Feller semigroups of operators determinated by systems of jumps dominated by the rotation invariant stable L\'evy measure. Using an approximation schema we prove the existence and obtain estimates of corresponding heat kernels.

We study existence and uniqueness of invariant probability measures for continuous-time Markov processes on general state spaces. Existence is obtained from tightness of time averages under a weak regularity assumption inspired by…

T. Szarek [Stud. Math. 189 (2008), {\S} 4] have discussed the relationship between two important notions concerning Markov semigroups: the asymptotic strong Feller property and the e-property, asserting that the former property implies the…

We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…

We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions and we show that…

We present conservativeness criteria for sub-Markovian semigroups generated by divergence type operators with specified infinitesimally invariant measures. The conservativeness criteria in this article are derived by $L^1$-uniqueness and…

If $(T_t)$ is a semigroup of Markov operators on an $L^1$-space that admits a non-trivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as $t \to \infty$. In this article we…

This work aims to investigate the well-posedness and the existence of ergodic invariant measures for a class of third grade fluid equations in bounded domain $D\subset\mathbb{R}^d,d=2,3,$ in the presence of a multiplicative noise. First, we…