Ergodicity for time-changed symmetric stable processes

DOI10.1016/j.spa.2014.04.003zbMath1328.60191arXiv1312.5042OpenAlexW1981330865MaRDI QIDQ740185

Jian Wang, Zhen-Qing Chen

Publication date: 2 September 2014

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.5042

zbMATH Keywords

stochastic differential equationsergodicityMarkov jump processesnon-local Dirichlet formsPoincaré type inequalitiestime-changed symmetric stable processes

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stable stochastic processes (60G52) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items

Necessary and sufficient conditions for ergodicity of CIR model driven by stable processes with Markov switching, Ergodicity of CIR type SDEs driven by stable processes with random switching, Ergodicity and transience of SDEs driven by -stable processes with Markovian switching, Exponential ergodicity for population dynamics driven by \(\alpha\)-stable processes, Ergodic convergence rates for time-changed symmetric Lévy processes in dimension one, Using Stein's method to analyze Euler-Maruyama approximations of regime-switching jump diffusion processes, Evolution systems of probability measures for nonautonomous Klein-Gordon Itô equations on \(\mathbb{Z}^N\), Approximation of stable law in Wasserstein-1 distance by Stein's method, Large deviations for multi-scale jump-diffusion processes, Exponential ergodicity for SDEs driven by \(\alpha\)-stable processes with Markovian switching in Wasserstein distances, Lyapunov-type conditions for non-strong ergodicity of Markov processes, Functional inequalities for time-changed symmetric \(\alpha \)-stable processes, Compactness and density estimates for weighted fractional heat semigroups, Convergence rates in uniform ergodicity by hitting times and \(L^2\)-exponential convergence rates, Dirichlet eigenvalues and exit time moments for symmetric Markov processes, Exponential and strong ergodicity for one-dimensional time-changed symmetric stable processes, Hölder continuity of semigroups for time changed symmetric stable processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dirichlet forms and symmetric Markov processes.
• On unique extension of time changed reflecting Brownian motions
• The quasi-sure ratio ergodic theorem
• On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations of jump type
• Exponential and uniform ergodicity of Markov processes
• Long-time behavior of stable-like processes
• Functional inequalities for empty essential spectrum
• On hyperboundedness and spectrum of Markov operators
• Weighted Poincaré inequalities for non-local Dirichlet forms
• Functional inequalities for nonlocal Dirichlet forms with finite range jumps or large jumps
• Criteria of spectral gap for Markov operators
• Heat kernel estimates for jump processes of mixed types on metric measure spaces
• Entropies, convexity, and functional inequalities: on \(\Phi\)-entropies and \(\Phi\)-Sobolev inequalities
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• Non-local Dirichlet forms and symmetric jump processes
• Eigenvalues, Inequalities, and Ergodic Theory