Exponential rate of convergence for some Markov operators

Abstract

The exponential rate of convergence for some Markov operators is established. The operators correspond to continuous iterated function systems which are a very useful tool in some cell cycle models.

17 pages. arXiv admin note: text overlap with arXiv:1506.07041

References in corpus (1)

• Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations

Cited by in corpus (9)

• Ergodic properties of some piecewise-deterministic Markov process with application to gene expression modelling
• A Useful Version of the Central Limit Theorem for a General Class of Markov Chains
• Limit Theorems for Some Markov Operators
• The Strassen Invariance Principle for Certain Non-stationary Markov-Feller Chains
• Law of the Iterated Logarithm for some Markov operators
• Exponential ergodicity in the bounded-Lipschitz distance for a subclass of piecewise-deterministic Markov processes with random switching between flows
• The central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm
• Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process
• The law of the iterated logarithm for a piecewise deterministic Markov process assured by the properties of the Markov chain given by its post-jump locations