The algebra of reversible Markov chains

weak-reversible Markov chains

The theory of L-spectral gaps for reversible Markov chains has been studied by many authors. In this paper we consider positive recurrent general state space Markov chains with stationary transition probabilities. Replacing the assumption of reversibility by a less strong one, we still obtain a simple necessary and sufficient condition for the spectral gap property of the associated Markov oper...

Chapter 3 Reversible Markov Chains

Chapter 2 reviewed some aspects of the elementary theory of general nite irreducible Markov chains. In this chapter we specialize to reversible chains, treating the discrete and continuous-time cases in parallel. After section 3 we shall assume that we are dealing with reversible chains without continually repeating this assumption, and shall instead explicitly say \general" to mean not-necessa...

Process Algebra and Markov Chains

This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study the interrelation of reactive processes and Markov chains in this setting, and introduce the algebr...

On Non-reversible Markov Chains

Reversibility is a suucient but not necessary condition for Markov chains for use in Markov chain Monte Carlo simulation. It is necessary to select a Markov chain that has a pre-speciied distribution as its unique stationary distribution. There are many Markov chains that have such property. We give guidelines on how to rank them based on the asymptotic variance of the estimates they produce. T...

Linear Algebra Application~ Markov Chains