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arXiv 2003.106142020-03math.PR

A Note on Subexponential Rate of Convergence to Equilibrium for Processes on the Half-Line

Andrey Sarantsev

备注：: 14 pages. Keywords: reflection mapping, Levy process, Lyapunov function, convergence rate, total variation, stochastic differential equation

英文摘要：

A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the half-line, Lyapunov functions can be used to easily find explicit rates of convergence. Our earlier research focused on exponential rate of convergence. This note extends these results to slower rates, including power rates, thus improving results of (Douc, Fort, Guillin, 2009).

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