Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Chair/Advisor

Robert Lund

Committee Member

Peter Kiessler

Committee Member

Andrew Brown

Committee Member

Brian Fralix


Explicit convergence rates to equilibrium are established for non reversible Markov chains not having an atom via coupling methods. We consider two Markov chains having the same transition function but different initial conditions on the same probability space, that is, a coupling. A random time is constructed so that subsequent to the random time the two processes are identical. Exploiting a shadowing condition, we show that it is possible to bound the tail distribution of the random time using only one of the chains. This bound gives the convergence rate to equilibrium for the Markov chain. The method is then applied to two examples; a storage model and a Gaussian auto regressive model.

Included in

Probability Commons



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