We consider a class of generalized Fibonacci unimodal maps for which the central return times {Sn} satisfy that sn= sn-1 ＋ ksh-2 for some k≥ 1. We show that such a unimodal map admits a unique absolutely continuous...We consider a class of generalized Fibonacci unimodal maps for which the central return times {Sn} satisfy that sn= sn-1 ＋ ksh-2 for some k≥ 1. We show that such a unimodal map admits a unique absolutely continuous invariant probability with exactly stretched exponential decay of correlations if its critical order lies in （1, k ＋ 1）.展开更多
We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation spac...We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation space, we also give an invariance principle for LIL. In some sense, this result is an extension of the classical Strassen's invariance principle to the case where probability measure is no longer additive. Furthermore,we give some examples as applications.展开更多
We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As an application, the 2D Navier-Stokes equations with degenerate stochastic fo...We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As an application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply revisited.展开更多
基金supported by AcRF-Tier 1 grant from MOE,Singapore(Grant No.R-146-000-199-112)
文摘We consider a class of generalized Fibonacci unimodal maps for which the central return times {Sn} satisfy that sn= sn-1 ＋ ksh-2 for some k≥ 1. We show that such a unimodal map admits a unique absolutely continuous invariant probability with exactly stretched exponential decay of correlations if its critical order lies in （1, k ＋ 1）.
基金supported by China Postdoctoral Science Foundation(Grant No.2013M541899)the Natural Science Foundation of Shandong Province of China(Grant Nos.ZR2013AQ021 and ZR2014AM002)+1 种基金National Natural Science Foundation of China(Grant Nos.11471190,11401414 and 11231005)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20140299)
文摘We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation space, we also give an invariance principle for LIL. In some sense, this result is an extension of the classical Strassen's invariance principle to the case where probability measure is no longer additive. Furthermore,we give some examples as applications.
基金supported by the Financial Support from Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant Nos.2008DP173182 and Y129161ZZ1)National Natural Science Foundation of China(Grant Nos.11021161 and 11201456)National Program on Key Basic Research Project of China(973 Program)(Grant No.2011CB808000)
文摘We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As an application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply revisited.
