Convergence of symmetric Markov chains on \({\mathbb{Z}^d}\)

DOI10.1007/s00440-009-0224-8zbMath1200.60060arXiv0807.3268OpenAlexW1656964588MaRDI QIDQ5961958

Takashi Kumagai, Toshihiro Uemura, Richard F. Bass

Publication date: 16 September 2010

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.3268

zbMATH Keywords

weak convergenceDirichlet formelliptic diffusionsymmetric Markov chain

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items (10)

Markov chain approximation of pure jump processes ⋮ Regularity of harmonic functions for some Markov chains with unbounded range ⋮ A class of singular symmetric Markov processes ⋮ De Giorgi type results for equations with nonlocal lower-order terms ⋮ Markov chain approximations for nonsymmetric processes ⋮ Discrete approximation of symmetric jump processes on metric measure spaces ⋮ Markov Chain Approximations to Nonsymmetric Diffusions with Bounded Coefficients ⋮ A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps ⋮ Convergence of Brownian motions on metric measure spaces under Riemannian curvature-dimension conditions ⋮ Homogenization of symmetric Dirichlet forms

Cites Work

• Unnamed Item
• An invariance principle for reversible Markov processes. Applications to random motions in random environments
• Symmetric jump processes: localization, heat kernels and convergence
• A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps
• Heat kernel estimates and Harnack inequalities for some Dirichlet forms with non-local part
• Upper bounds for symmetric Markov transition functions
• Dirichlet forms and symmetric Markov processes
• Markov chain approximations to symmetric diffusions
• Markov chain approximations for symmetric jump processes
• Heat kernel estimates for jump processes of mixed types on metric measure spaces
• Heat kernel estimates for stable-like processes on \(d\)-sets.
• Non-local Dirichlet forms and symmetric jump processes
• Symmetric Markov chains on ℤ^{𝕕} with unbounded range

This page was built for publication: Convergence of symmetric Markov chains on \({\mathbb{Z}^d}\)