Subgeometric rates of convergence for Markov processes under subordination

Understand

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 moments (sub-exponential, algebraic and logarithmic) for subordinators as time $t$ tends to infinity.
• At the end we discuss some concrete models and we show that subordination can dramatically change the speed of convergence to equilibrium.