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Spectral Analysis of Markov Kernels and Application to the Convergence Rate Of Discrete Random Walks
- Part of
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- Journal:
- Advances in Applied Probability / Volume 46 / Issue 4 / December 2014
- Published online by Cambridge University Press:
- 22 February 2016, pp. 1036-1058
- Print publication:
- December 2014
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- Article
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Let {Xn}n∈ℕ be a Markov chain on a measurable space
with transition kernel P, and let 
The Markov kernel P is here considered as a linear bounded operator on the weighted-supremum space 
associated with V. Then the combination of quasicompactness arguments with precise analysis of eigenelements of P allows us to estimate the geometric rate of convergence ρV(P) of {Xn}n∈ℕ to its invariant probability measure in operator norm on 
A general procedure to compute ρV(P) for discrete Markov random walks with identically distributed bounded increments is specified.
with transition kernel 
The Markov kernel 
associated with 
A general procedure to compute ρ