## Approximating Countable Markov Chains |

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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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### Common terms and phrases

Abbreviate absorbing argument binary rational Borel chain with stationary chapter Claim coincides communicating class construction coordinate process defined definition disjoint empty product exponentially distributed Figure finite subset follows Fubini given hitting holding implies independent and exponentially interval of constancy joint distribution jump least Lebesgue measure Lemma Let F Let Q locally finitary Markov chain Markov property Markov with stationary Markov with transitions martingale measurable function measurable mapping nondecreasing notation null set P,-distribution Poisson Poisson process positive recurrent post-r process Prob probability triple prove Pt{A Q(co quasiregular r-field spanned random variable real number recurrent class regular conditional distribution retracted sample functions satisfies Section sequence signed measure smallest r-field standard stochastic semigroup starting stationary transitions step functions stochastic matrix strong Markov property Theorem valued visits yj(t