Subexponential upper and lower bounds in Wasserstein distance for Markov processes

DOI10.1007/s00245-022-09866-zzbMath1497.60097arXiv1907.05250OpenAlexW3009255692MaRDI QIDQ2674434

Nikola Sandrić, Guodong Pang, Aristotle Arapostathis

Publication date: 12 September 2022

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.05250

zbMATH Keywords

Ornstein-Uhlenbeck processWasserstein distanceItô processFoster-Lyapunov conditionasymptotic flatness (uniform dissipativity)exponential and subexponential ergodicityLangevin diffusion process

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Discrete-time Markov processes on general state spaces (60J05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Jump processes on general state spaces (60J76)

Related Items (2)

Hoeffding's inequality for non-irreducible Markov models ⋮ Birth and death processes in interactive random environments

Cites Work

• Unnamed Item
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• Ergodicity and fluctuations of a fluid particle driven by diffusions with jumps
• \(L^{p}\)-Wasserstein distance for stochastic differential equations driven by Lévy processes
• Heat kernels and analyticity of non-symmetric jump diffusion semigroups
• Reflection couplings and contraction rates for diffusions
• Positive recurrence of piecewise Ornstein-Uhlenbeck processes and common quadratic Lyapunov functions
• Central limit theorem for Markov processes with spectral gap in the Wasserstein metric
• On the coupling property and the Liouville theorem for Ornstein-Uhlenbeck processes
• Densities for SDEs driven by degenerate \(\alpha\)-stable processes
• Subgeometric rates of convergence in Wasserstein distance for Markov chains
• Subgeometric ergodicity of strong Markov processes
• Reflection coupling and Wasserstein contractivity without convexity
• Coupling for Ornstein-Uhlenbeck processes with jumps
• Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type
• Ergodicity and exponential \(\beta\)-mixing bounds for multidimensional diffusions with jumps
• Subgeometric ergodicity for continuous-time Markov chains
• Erratum to: On the existence of smooth densities for jump processes
• Existence of global solutions and invariant measures for stochastic differential equations driven by Poisson type noise with non-Lipschitz coefficients
• Exponential ergodicity of the solutions to SDE's with a jump noise
• Erratum to: ``Ergodicity and exponential \(\beta \)-mixing bound for multidimensional diffusions with jumps
• Subgeometric rates of convergence of \(f\)-ergodic strong Markov processes
• State-dependent Foster-Lyapunov criteria for subgeometric convergence of Markov chains
• The Malliavin calculus for pure jump processes and applications to local time
• On polynomial mixing bounds for stochastic differential equations
• A note on Hurwitz stability of matrices
• Topological conditions enabling use of Harris methods in discrete and continuous time
• On multidimensional Ornstein-Uhlenbeck processes driven by a general Lévy process
• Heat kernels for time-dependent non-symmetric stable-like operators
• Parametrix construction of the transition probability density of the solution to an SDE driven by \(\alpha\)-stable noise
• Heat kernels of non-symmetric jump processes: beyond the stable case
• Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes
• Ergodic properties of generalized Ornstein-Uhlenbeck processes
• Jump type stochastic differential equations with non-Lipschitz coefficients: non-confluence, Feller and strong Feller properties, and exponential ergodicity
• Ergodicity of a Lévy-driven SDE arising from multiclass many-server queues
• On martingale problems and Feller processes
• Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations
• Practical drift conditions for subgeometric rates of convergence.
• Exponential and uniform ergodicity of Markov processes
• Existence of strong solutions for Itô's stochastic equations via approximations
• On the existence of smooth densities for jump processes
• Heat kernels of non-symmetric jump processes with exponentially decaying jumping kernel
• Periodic homogenization of a Lévy-type process with small jumps
• Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise
• Heat kernel for non-local operators with variable order
• Existence of (Markovian) solutions to martingale problems associated with Lévy-type operators
• On sub-geometric ergodicity of diffusion processes
• Heat kernels of non-symmetric Lévy-type operators
• Subgeometric rates of convergence for discrete-time Markov chains under discrete-time subordination
• Uniform polynomial rates of convergence for a class of Lévy-driven controlled SDEs arising in multiclass many-server queues
• Ergodic behavior of Markov processes. With applications to limit theorems
• Heat kernels for non-symmetric diffusion operators with jumps
• Transition density estimates for a class of Lévy and Lévy-type processes
• Markov processes, semigroups and generators.
• Subgeometric rates of convergence of Markov processes in the Wasserstein metric
• Polynomial ergodicity of Markov transition kernels.
• On Polynomial Mixing and Convergence Rate for Stochastic Difference and Differential Equations
• Long-time behavior for a class of Feller processes
• Exponential convergence in Lp-Wasserstein distance for diffusion processes without uniformly dissipative drift
• Quantitative Convergence Rates for Subgeometric Markov Chains
• A piecewise linear stochastic differential equation driven by a Lévy process
• Ergodic Control of Diffusion Processes
• Stability of Markovian processes II: continuous-time processes and sampled chains
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• Markov Chains and Stochastic Stability
• Homogenization of a Class of Integro-Differential Equations with Lévy Operators
• [https://portal.mardi4nfdi.de/wiki/Publication:4043914 Diffusion processes associated with L�vy generators]
• Subgeometric Rates of Convergence of f-Ergodic Markov Chains
• Symmetric Stable Laws and Stable-Like Jump-Diffusions
• Eigenvalues, Inequalities, and Ergodic Theory
• Strong feller property and irreducibility of diffusions with jumps
• On the Exponential Ergodicity of Lévy-Driven Ornstein–Uhlenbeck Processes
• A note on the existence of transition probability densities of Lévy processes
• On Uniform Exponential Ergodicity of Markovian Multiclass Many-Server Queues in the Halfin–Whitt Regime
• Subgeometric rates of convergence for Markov processes under subordination - Correction
• Subgeometric rates of convergence for Markov processes under subordination
• A subgeometric estimate of the stability for time-homogeneous Markov chains
• Bernstein functions. Theory and applications
• Optimal Transport
• Density estimate in small time for jump processes with singular Lévy measures

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