Abstract
Generally, the convergence rate in \(L^2\)-exponential ergodicity \(\lambda \) is an upper bound for the convergence rate \(\kappa \) in uniform ergodicity for a Markov process, that is, \(\lambda \geqslant \kappa \). In this paper, we prove that \(\kappa \geqslant \inf \left\{ \lambda ,1/M_H\right\} \), where \(M_H\) is a uniform bound on the moment of the hitting time to a “compact” set H. In the case where \(M_H\) can be made arbitrarily small for H large enough. we obtain that \(\lambda =\kappa \). The general results are applied to Markov chains, diffusion processes and solutions to stochastic differential equations driven by symmetric stable processes.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.