This paper is concerned with the convergence rates of ergodic limits and approximation for regularized resolvent families for a linear Volterra integral equation. The results contain C 0-semigroups, cosine operator fu...This paper is concerned with the convergence rates of ergodic limits and approximation for regularized resolvent families for a linear Volterra integral equation. The results contain C 0-semigroups, cosine operator functions and α-times integrated resolvent family as special cases.展开更多
Let p≥2 be a prime number and Zp be the ring of p-adic intergers.Let G be a semigroup generated by infinitely many contractive maps on p Zp.It is shown that if G satisfies the open tiling conditions,then there exists...Let p≥2 be a prime number and Zp be the ring of p-adic intergers.Let G be a semigroup generated by infinitely many contractive maps on p Zp.It is shown that if G satisfies the open tiling conditions,then there exists a shift transformation on the limit set of G and the shift transformation is ergodic with respect to the Haar measure on p Zp.As an application,we can generalize p-adic Khinchin’s Theorem and p-adic Lochs’Theorem to any infinitely generated semigroup by use of the ergodicity of the shift transformation.展开更多
The present paper is devoted to a preliminary study towards the establishment of an ergodic theory for stochastic di erential equations(SDEs)with less regular coecients and degenerate noises.These equations are often ...The present paper is devoted to a preliminary study towards the establishment of an ergodic theory for stochastic di erential equations(SDEs)with less regular coecients and degenerate noises.These equations are often derived as mesoscopic limits of complex or huge microscopic systems.By studying the associated Fokker-Planck equation(FPE),we prove the convergence of the time average of globally de ned weak solutions of such an SDE to the set of stationary measures of the FPE under Lyapunov conditions.In the case where the set of stationary measures consists of a single element,the unique stationary measure is shown to be physical.Similar convergence results for the solutions of the FPE are established as well.Some of our convergence results,while being special cases of those contained in Ji et al.(2019)for SDEs with periodic coecients,have weaken the required Lyapunov conditions and are of much simpli ed proofs.Applications to stochastic damping Hamiltonian systems and stochastic slow-fast systems are given.展开更多
Let X be a compact metric space studies some relationships between stochastic and f ： X→ X be a continuous map. This paper and topological properties of dynamical systems. It is shown that if f satisfies the central...Let X be a compact metric space studies some relationships between stochastic and f ： X→ X be a continuous map. This paper and topological properties of dynamical systems. It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and / is sensitively dependent on initial conditions if and only if / is neither minimal nor equicontinuous.展开更多
记=f1×f2×…×fn,n={1,2,…,n},=X1×X2×…×Xn,本文给出了是拓扑遍历的两个充要条件。若fi有POTP,Xi是连通的,i∈n,则是拓扑遍历的27个等价条件被给出。讨论了是拓扑遍历的一些充分条件和必...记=f1×f2×…×fn,n={1,2,…,n},=X1×X2×…×Xn,本文给出了是拓扑遍历的两个充要条件。若fi有POTP,Xi是连通的,i∈n,则是拓扑遍历的27个等价条件被给出。讨论了是拓扑遍历的一些充分条件和必要条件。设fi∈C0(Xi,Xi),Xi为紧度量空间,i∈n,证明了:①若是拓扑遍历的,则■1×…×■n∶M(X1)×…×M(Xn)→M(X1)×…×M(Xn)是拓扑遍历的。②设(X∞(j),f∞(j))为由{Xi(j),gi(j),fi(j)}∞i=1生成的逆极限系统,j∈n,则f∞(1)×…×f∞(n)为拓扑遍历的当且仅当multiply from j=1 to n fi(j)(i=1,2,…)均为拓扑遍历的。③若存在j∈n,使得对t∈n且t≠j,ft均为拓扑混合的,则是拓扑遍历的当且仅当fj是拓扑遍历的。展开更多
In this paper we give the necessary and sufficient conditions for all finite critical points of quadratic differential systems to be weak foci, and solve an open problem proposed by Yanqian Ye.
We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The co...We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented.展开更多
基金This project is supported by the Special Funds for Major Specialties of Shanghai Education Committee and the Natural Foundation ofShanghai City.
文摘This paper is concerned with the convergence rates of ergodic limits and approximation for regularized resolvent families for a linear Volterra integral equation. The results contain C 0-semigroups, cosine operator functions and α-times integrated resolvent family as special cases.
基金Supported by Natural Science Foundation of China(Grant Nos.11301510,11671092)。
文摘Let p≥2 be a prime number and Zp be the ring of p-adic intergers.Let G be a semigroup generated by infinitely many contractive maps on p Zp.It is shown that if G satisfies the open tiling conditions,then there exists a shift transformation on the limit set of G and the shift transformation is ergodic with respect to the Haar measure on p Zp.As an application,we can generalize p-adic Khinchin’s Theorem and p-adic Lochs’Theorem to any infinitely generated semigroup by use of the ergodicity of the shift transformation.
基金The first author was supported by China Scholarship Council.The second author was supported by University of Alberta,and Natural Sciences and Engineering Research Council of Canada(Grant Nos.RGPIN-2018-04371 and DGECR-2018-00353)The third author was supported by Pacific Institute for the Mathematical Sciences-Canadian Statistical Sciences Institute Postdoctoral Fellowship,Pacific Institute for the Mathematical Sciences-Collaborative Research Group Grant,National Natural Science Foundation of China(Grant Nos.11771026 and 11471344)+2 种基金the Pacific Institute for the Mathematical Sciences-University of Washington site through National Science Foundation of USA(Grant No.DMS-1712701)The fourth author was supported by Natural Sciences and Engineering Research Council of Canada Discovery(Grant No.1257749)Pacific Institute for the Mathematical Sciences-Collaborative Research Group Grant,University of Alberta,and Jilin University.
文摘The present paper is devoted to a preliminary study towards the establishment of an ergodic theory for stochastic di erential equations(SDEs)with less regular coecients and degenerate noises.These equations are often derived as mesoscopic limits of complex or huge microscopic systems.By studying the associated Fokker-Planck equation(FPE),we prove the convergence of the time average of globally de ned weak solutions of such an SDE to the set of stationary measures of the FPE under Lyapunov conditions.In the case where the set of stationary measures consists of a single element,the unique stationary measure is shown to be physical.Similar convergence results for the solutions of the FPE are established as well.Some of our convergence results,while being special cases of those contained in Ji et al.(2019)for SDEs with periodic coecients,have weaken the required Lyapunov conditions and are of much simpli ed proofs.Applications to stochastic damping Hamiltonian systems and stochastic slow-fast systems are given.
基金Support by the Natural Science Foundation of Anhui Educational Committee (KJ2007B123)863 Project(2007AA03Z108)
文摘Let X be a compact metric space studies some relationships between stochastic and f ： X→ X be a continuous map. This paper and topological properties of dynamical systems. It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and / is sensitively dependent on initial conditions if and only if / is neither minimal nor equicontinuous.
文摘记=f1×f2×…×fn,n={1,2,…,n},=X1×X2×…×Xn,本文给出了是拓扑遍历的两个充要条件。若fi有POTP,Xi是连通的,i∈n,则是拓扑遍历的27个等价条件被给出。讨论了是拓扑遍历的一些充分条件和必要条件。设fi∈C0(Xi,Xi),Xi为紧度量空间,i∈n,证明了:①若是拓扑遍历的,则■1×…×■n∶M(X1)×…×M(Xn)→M(X1)×…×M(Xn)是拓扑遍历的。②设(X∞(j),f∞(j))为由{Xi(j),gi(j),fi(j)}∞i=1生成的逆极限系统,j∈n,则f∞(1)×…×f∞(n)为拓扑遍历的当且仅当multiply from j=1 to n fi(j)(i=1,2,…)均为拓扑遍历的。③若存在j∈n,使得对t∈n且t≠j,ft均为拓扑混合的,则是拓扑遍历的当且仅当fj是拓扑遍历的。
基金The project is partially supported by the National Natural Foundation of China with the grant number 10901013.
文摘In this paper we give the necessary and sufficient conditions for all finite critical points of quadratic differential systems to be weak foci, and solve an open problem proposed by Yanqian Ye.
基金Acknowledgements The authors would like to thank Professor Yong-Hua Mao for useful discussion. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11571372, 11501576, 11771452） and the Excellent Young Scientific Research Fund of Hunan Provincial Education Department （Grant No. 15B252）.
文摘We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented.
