## Approximating countable Markov chainsThe book, part of a trilogy covering the field of Markov processes, explains one method of approximating countable Markov chains by finite ones. Intended for use in seminars with advanced graduate students, it is written in the framework of the first book in the trilogy, Markov Chains, although it is completely independent of the second, Brownian Motion and Diffusion. The idea is to skip over the times at which the chain is outside some large, finite set of states. The technique is especially useful for dealing with instantaneous states. Many of the results are original. (Author). |

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### Contents

RESTRICTING THE RANGE | 1 |

RESTRICTING THE RANGE APPLICATIONS | 64 |

CONSTRUCTING THE GENERAL MARKOV CHAIN | 95 |

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### Common terms and phrases

Abbreviate absorbing Amer argue argument binary rationals Brownian Motion chapter claim coincides conditional distribution constancy for Xj construction converges Countable Markov Chains David Freedman defined difference quotient exponentially distributed Figure finite subset follows Fubini Hj(t holding implies independent and exponential infinite interval of constancy joint distribution jointly measurable jump kind appears l)-intervals Lebesgue measure Lemma Let f Let Q locally finitary Markov process Markov with stationary Markov with transitions Math notation null set Poisson process Poisson with parameter positive Prdistribution Prob product measurable Prprobability pseudo-jumps Pt{A Qj(i QN+m quasiregular r-field random variables recurrent restriction retracted sample functions satisfy 1-2 sequence sigma field spends interior standard stochastic semigroup starting stationary standard transitions stationary transitions step functions strictly increasing strong Markov MC Suppose Theorem visits Volker Strassen William Feller Xj(t yj(s yj(Sm yj(t YN+m