On ergodic property of some Lévy-type processes in Rd
DOI:
https://doi.org/10.17721/1812-5409.2026/1.8Keywords:
Lévy-type process, Lyapunov criterion, Lyapunov function, ergodicityAbstract
In this paper, we investigate the ergodicity in total variation of the process X, related to some integro-differential operator with unbounded coefficients, and describe the speed of convergence to the respective invariant measure. Roughly speaking, a Markov process is said to be ergodic if there exists an invariant probability measure to which the transition probability of the considered process converges. In this case, the speed of convergence is also called the ergodic rate, and it plays an important role in further investigations of asymptotic properties, in particular, in simulating the processes, calculating their functionals, and also in limit theorems.
In the proofs, we use the Lyapunov-type criterion, which resembles the well-known from the theory of ordinary differential equations Lyapunov’s second method. Some examples are provided.
Pages of the article in the issue: 63 - 71
Language of the article: English
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