An introduction to Markov processes

"This book provides an introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering, economics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes. A whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium, and these considerations are applied to an analysis of the efficiency of the Metropolis algorithm. For the convenience of the reader, the final chapter gives a resume of the requisite ideas from measure theory."--Jacket. 
Random Walks a Good Place to Begin.- Doeblin's Theory for Markov Chains.- More about the Ergodic Theory of Markov Chains.- Markov Processes in Continuous Time.- Reversible Markov Processes.- Some Mild Measure Theory.- Notation.- References.- Index