## 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 |

Copyright | |

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Abbreviate absorbing Amer Approximating Countable Markov argue argument binary rationals Brownian Motion chapter claim coincides conditional distribution construction converges Countable Markov Chains David Freedman Define deleting a null difference quotient exponentially distributed Figure finite subset Fubini Hj(t holding implies independent and exponential infinite interval of constancy joint distribution jointly measurable jump kind appears l)-intervals Lebesgue measure Lebesgue s:0 Lemma Let F Let Xj locally finitary Markov process Markov with stationary Markov with transitions Math notation null set Pi{A Pj(t Poisson process Poisson with parameter positive Prdistribution Prob product measurable Prprobability pseudo-jumps qj(i QN(j QN+m quasiregular random variables recurrent restriction retracted sample functions satisfy 1-2 sequence sigma field spends interior standard stochastic semigroup starting stationary standard transitions stationary transitions strictly increasing strong Markov MC Theorem visits Volker Strassen William Feller X-scale Xf(t Xj(t yj(s yj(t yn(t YN+m