Markov chains and processes with a prescribed invariant measure

Identifying Markov Chains with a Given Invariant Measure

Ergodic Theory of Markov Chains Admitting an Infinite Invariant Measure.

Markov Chains and Jump Processes

Lecture-25: Markov Chains: Invariant Distribution

Theorem 1.1. An irreducible Markov chain with transition probability matrix P is positive recurrent iff there exists a unique invariant probability measure π on state space S that satisfies global balance equation π = πP and πi = 1 μii > 0 for all i ∈ S. Proof. Let X be a positive recurrent Markov chain on state space S, with X0 = i. Let Hi be the first recurrence time to state i, and let N j(n...

Markov Chains and De-initialising Processes

We define a notion of de-initialising Markov chains. We prove that to analyse convergence of Markov chains to stationarity, it suffices to analyse convergence of a deinitialising chain. Applications are given to Markov chain Monte Carlo algorithms and to convergence diagnostics.