Abstract
In the analytic approach to Markov chains, the convergence to steady state of an ergodic hmc is a consequence of a result on power series called the renewal theorem by the probabilists. In this chapter however the renewal theorem will not be the essential step in the proof of the convergence theorem but, on the contrary, it will be obtained as a corollary of the latter.
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Brémaud, P. (2020). Discrete-Time Renewal Theory. In: Markov Chains. Texts in Applied Mathematics, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-030-45982-6_5
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DOI: https://doi.org/10.1007/978-3-030-45982-6_5
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-45982-6
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