ON ERGODICITY OF SOME MARKOV PROCESSES

• 成果类型: Article
• 署名作者: Komorowski, Tomasz; Peszat, Szymon; Szarek, Tomasz
• 署名单位: Maria Curie-Sklodowska University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Fahrenheit Universities; University of Gdansk
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP513
• 发表日期: 2010
• 页码: 1401-1443
• 关键词: navier-stokes equations; passive tracer; DYNAMICS; SPACES

摘要

We formulate a criterion for the existence and uniqueness of an invariant measure for a Markov process taking values in a Polish phase space In addition. weak-* ergodicity, that is, the weak convergence of the ergodic averages of of the laws of the process starting from any initial distribution, is established The principal assumptions are the existence of a lower bound for the ergodic averages of the transition probability function and its local uniform continuity The latter is called the e-property The general result is applied to solutions of sonic stochastic evolution equations in Hilbert spaces. As an example, we consider an evolution equation whose solution describes the Lagrangian observations of the velocity field in the passive tracer model The weak-* mean ergodicity of the corresponding invariant measure is used to derive the law of large numbers for the trajectory of a tracer