Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Quasi-compactness of Markov kernels on weighted-supremum spaces and geometrical ergodicity (1110.3240v5)

Published 14 Oct 2011 in math.PR

Abstract: Let $P$ be a Markov kernel on a measurable space $\X$ and let $V:\X\r[1,+\infty)$. We provide various assumptions, based on drift conditions, under which $P$ is quasi-compact on the weighted-supremum Banach space $(\cB_V,|\cdot|V)$ of all the measurable functions $f : \X\r\C$ such that $|f|_V := \sup{x\in \X} |f(x)|/V(x) < \infty$. Furthermore we give bounds for the essential spectral radius of $P$. Under additional assumptions, these results allow us to derive the convergence rate of $P$ on $\cB_V$, that is the geometric rate of convergence of the iterates $Pn$ to the stationary distribution in operator norm. Applications to discrete Markov kernels and to iterated function systems are presented.

Summary

We haven't generated a summary for this paper yet.