## Approximating countable Markov chains |

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### Contents

RESTRICTING THE RANGE | 1 |

RESTRICTING THE RANGE APPLICATIONS | 64 |

CONSTRUCTING THE GENERAL MARKOV CHAIN | 95 |

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Abbreviate absorbing Amer argue argument binary rationals Brownian motion chapter claim coincides conditional distribution construction converges Define difference quotient exponentially distributed Figure fij(t finite subset Fix i e follows Fubini holding i)-measurable 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 locally finitary Markov chain Markov process Markov property MC Markov with stationary Markov with transitions Math nonnegative numbers notation null set parameter q Poisson process Poisson with parameter positive Prdistribution Prob product measurable Prprobability pseudo-jumps Q„+i quasiregular random variables recurrent restriction retracted S(co 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(t YN+m