Subgeometric rates of convergence for Markov processes under subordination
TLDR
In this paper, the authors studied the convergence rate of a Markov process to its invariant measure with a subordinator and the corresponding Bernstein function and showed that subordination can dramatically change the speed of convergence to equilibrium.Abstract:
We are interested in the rate of convergence of a subordinate Markov process to its invariant measure. Given a subordinator and the corresponding Bernstein function (Laplace exponent), we characterize the convergence rate of the subordinate Markov process; the key ingredients are the rate of convergence of the original process and the (inverse of the) Bernstein function. At a technical level, the crucial point is to bound three types of moment (subexponential, algebraic, and logarithmic) for subordinators as time t tends to ∞. We also discuss some concrete models and we show that subordination can dramatically change the speed of convergence to equilibrium.read more
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Convolution inequalities for Besov and Triebel--Lizorkin spaces, and applications to convolution semigroups
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Subexponential upper and lower bounds in Wasserstein distance for Markov processes
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Bochner's Subordionation and Fractional Caloric Smoothing in Besov and Triebel--Lizorkin Spaces.
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References
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Book
Markov Chains and Stochastic Stability
Sean P. Meyn,Richard L. Tweedie +1 more
TL;DR: This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.
Journal ArticleDOI
Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
Sean P. Meyn,Richard L. Tweedie +1 more
TL;DR: In this paper, the authors developed criteria for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the extended generator, and applied the criteria to several specific processes, including linear stochastic systems under nonlinear feedback, work-modulated queues, general release storage processes and risk processes.
Book
From Markov Chains to Non-Equilibrium Particle Systems
TL;DR: In this paper, a representative work of Chinese probabilists on probability theory and its applications in physics is presented, including the results of jump Markov processes, as well as Markov interacting processes with noncompact states.
Book
Bernstein Functions: Theory and Applications
TL;DR: In this paper, the authors present a self-contained and unified approach to Bernstein functions and closely related function classes, bringing together old and establishing new connections, and an extensive list of complete Bernstein functions with their representations is provided.
Journal ArticleDOI
Stability of Markovian processes II: continuous-time processes and sampled chains
Sean P. Meyn,Richard L. Tweedie +1 more
TL;DR: In this paper, the authors extend the results of Meyn and Tweedie (1992b) from discrete-time parameter to continuous-parameter Markovian processes evolving on a topological space, and prove connections between these and standard probabilistic recurrence concepts.