The Experts below are selected from a list of 8274 Experts worldwide ranked by ideXlab platform
Arnaud Guillin - One of the best experts on this subject based on the ideXlab platform.
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Hitting times, functional inequalities, Lyapunov conditions and uniform ergodicity
Journal of Functional Analysis, 2017Co-Authors: Patrick Cattiaux, Arnaud GuillinAbstract:The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was shown in [4, 30] that there is an equivalence between a Poincare inequality, the existence of some Lyapunov function and the exponential integrability of hitting times. In the present paper, we close the scheme of the interplay between Lyapunov conditions and functional inequalities by • showing that strong functional inequalities are equivalent to Lyapunov type conditions; • showing that these Lyapunov conditions are characterized by the finiteness of generalized exponential moments of hitting times. We also give some complement concerning the link between Lyapunov conditions and in-tegrability property of the Invariant Probability Measure and as such transportation inequalities , and we show that some " unbounded Lyapunov conditions " can lead to uniform ergodicity, and coming down from infinity property.
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Hitting times, functional inequalities, lyapunov conditions and uniform ergodicity
arXiv: Probability, 2016Co-Authors: Patrick Cattiaux, Arnaud GuillinAbstract:The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was shown in [4, 30] that there is an equivalence between a Poincar{\'e} inequality, the existence of some Lyapunov function and the exponential integrability of hitting times. In the present paper, we close the scheme of the interplay between Lyapunov conditions and functional inequalities by $\bullet$ showing that strong functional inequalities are equivalent to Lyapunov type conditions; $\bullet$ showing that these Lyapunov conditions are characterized by the finiteness of generalized exponential moments of hitting times. We also give some complement concerning the link between Lyapunov conditions and in-tegrability property of the Invariant Probability Measure and as such transportation inequalities , and we show that some "unbounded Lyapunov conditions" can lead to uniform ergodicity, and coming down from infinity property.
Patrick Cattiaux - One of the best experts on this subject based on the ideXlab platform.
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Hitting times, functional inequalities, Lyapunov conditions and uniform ergodicity
Journal of Functional Analysis, 2017Co-Authors: Patrick Cattiaux, Arnaud GuillinAbstract:The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was shown in [4, 30] that there is an equivalence between a Poincare inequality, the existence of some Lyapunov function and the exponential integrability of hitting times. In the present paper, we close the scheme of the interplay between Lyapunov conditions and functional inequalities by • showing that strong functional inequalities are equivalent to Lyapunov type conditions; • showing that these Lyapunov conditions are characterized by the finiteness of generalized exponential moments of hitting times. We also give some complement concerning the link between Lyapunov conditions and in-tegrability property of the Invariant Probability Measure and as such transportation inequalities , and we show that some " unbounded Lyapunov conditions " can lead to uniform ergodicity, and coming down from infinity property.
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Hitting times, functional inequalities, lyapunov conditions and uniform ergodicity
arXiv: Probability, 2016Co-Authors: Patrick Cattiaux, Arnaud GuillinAbstract:The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was shown in [4, 30] that there is an equivalence between a Poincar{\'e} inequality, the existence of some Lyapunov function and the exponential integrability of hitting times. In the present paper, we close the scheme of the interplay between Lyapunov conditions and functional inequalities by $\bullet$ showing that strong functional inequalities are equivalent to Lyapunov type conditions; $\bullet$ showing that these Lyapunov conditions are characterized by the finiteness of generalized exponential moments of hitting times. We also give some complement concerning the link between Lyapunov conditions and in-tegrability property of the Invariant Probability Measure and as such transportation inequalities , and we show that some "unbounded Lyapunov conditions" can lead to uniform ergodicity, and coming down from infinity property.
Feng-yu Wang - One of the best experts on this subject based on the ideXlab platform.
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asymptotic log harnack inequality and applications for stochastic systems of infinite memory
Stochastic Processes and their Applications, 2019Co-Authors: Feng-yu Wang, Jianhai Bao, Chenggui YuanAbstract:Abstract The asymptotic log-Harnack inequality is established for several kinds of models on stochastic differential systems with infinite memory: non-degenerate SDEs, neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems. As applications, the following properties are derived for the associated segment Markov semigroups: asymptotic heat kernel estimate, uniqueness of the Invariant Probability Measure, asymptotic gradient estimate (hence, asymptotically strong Feller property), as well as asymptotic irreducibility.
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asymptotic log harnack inequality and applications for stochastic systems of infinite memory
arXiv: Probability, 2017Co-Authors: Feng-yu Wang, Jianhai Bao, Chenggui YuanAbstract:The asymptotic log-Harnack inequality is established for several different models of stochastic differential systems with infinite memory: non-degenerate SDEs, Neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems. As applications, the following properties are derived for the associated segment Markov semigroups: asymptotic heat kernel estimate; uniqueness of the Invariant Probability Measure; asymptotic gradient estimate and hence, asymptotically strong Feller property; and asymptotic irreducibilty.
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derivative formula and applications for hyperdissipative stochastic navier stokes burgers equations
arXiv: Probability, 2010Co-Authors: Feng-yu Wang, Lihu XuAbstract:By using coupling method, a Bismut type derivative formula is established for the Markov semigroup associated to a class of hyperdissipative stochastic Navier-Stokes/Burgers equations. As applications, gradient estimates, dimension-free Harnack inequality, strong Feller property, heat kernel estimates and some properties of the Invariant Probability Measure are derived.
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a harnack type inequality for non symmetric markov semigroups
Journal of Functional Analysis, 2006Co-Authors: Feng-yu WangAbstract:Abstract For a strong Feller and irreducible Markov semigroup on a locally compact Polish space, the Harnack-type inequality (1.1) holds if and only if the semigroup has a unique Invariant Probability Measure and is ultracontractive. Moreover, new sufficient conditions for this inequality to hold, as well as upper bound estimates of the underlying constant, are presented for diffusion semigroups on Riemannian manifolds.
Tony Jin - One of the best experts on this subject based on the ideXlab platform.
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Solution to the Quantum Symmetric Simple Exclusion Process: The Continuous Case
Communications in Mathematical Physics, 2021Co-Authors: Denis Bernard, Tony JinAbstract:The quantum symmetric simple exclusion process (Q-SSEP) is a model for quantum stochastic dynamics of fermions hopping along the edges of a graph with Brownian noisy amplitudes and driven out-of-equilibrium by injection-extraction processes at a few vertices. We present a solution for the Invariant Probability Measure of the one dimensional Q-SSEP in the infinite size limit by constructing the steady correlation functions of the system density matrix and quantum expectation values. These correlation functions code for a rich structure of fluctuating quantum correlations and coherences. Although our construction does not rely on the standard techniques from the theory of integrable systems, it is based on a remarkable interplay between the permutation groups and polynomials. We incidentally point out a possible combinatorial interpretation of the Q-SSEP correlation functions via a surprising connexion with geometric combinatorics and the associahedron polytopes.
Oscar Vegaamaya - One of the best experts on this subject based on the ideXlab platform.
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on the regularity property of semi markov processes with borel state spaces
2012Co-Authors: Oscar VegaamayaAbstract:This note shows that a semi-Markov process with Borel state space is regular under a fairly weak condition on the mean sojourn or holding times and assuming that the embedded Markov chain satisfies one of the following conditions: (a) it is Harris recurrent; (b) it is recurrent and the “recurrent part” of the state space is reached with Probability one for every initial state; (c) it has a unique Invariant Probability Measure. Under the latter condition, the regularity property is only ensured for almost all initial states with respect to the Invariant Probability Measure.
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a note on the regularity property of semi markov processes with borel state space
Social Science Research Network, 2002Co-Authors: Oscar VegaamayaAbstract:This note shows that a semi-Markov process with Borel state space is under a fairly weak condition on the or and assuming that the embedded Markov chain satisfies either one of the following conditions: (a) it is ; (b) it is and the “recurrent part” of the state space is reached with Probability one for every initial state; (c) it has a Under the latter condition, the regularity property is only ensured for almost all initial state with respect to the Invariant Probability Measure.
