Subgeometric rates of convergence for Markov processes under subordination

Research output: Contribution to journalResearch articleContributedpeer-review


  • Chang Song Deng - , Wuhan University (Author)
  • René L. Schilling - , Chair of Probability Theory (Author)
  • Yan Hong Song - , Zhongnan University of Economics and Law (Author)


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.


Original languageEnglish
Pages (from-to)162-181
Number of pages20
JournalAdvances in Applied Probability
Issue number1
Publication statusPublished - 1 Mar 2017



  • Bernstein function, invariant measure, Markov process, moment estimate, Rate of convergence, subordination