Approximating Countable Markov Chains |
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RESTRICTING THE RANGE | 1 |
RESTRICTING THE RANGE APPLICATIONS | 64 |
64 | 84 |
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Abbreviate absorbing appears argue argument begin binary rationals chapter choose claim Clearly coincides common completes conditional Confine construction converges corresponding countable course cuts defined definition depend distribution event exists exponential Figure finite finite subset follows force Fubini given hitting holding implies In+1 increasing independent infinite interval joint jump kind least Lebesgue Lemma limit Markov chain Markov with stationary Math means measurable nondecreasing nonnegative NOTE obtained P-distribution P-probability parameter Poisson positive Prob probability probability triple PROOF prove quasiregular random variables Recall recurrent relation relative Remember restriction result right continuous sample functions satisfies Section sequence shows side spends standard stochastic semigroup starting strictly strong Markov Suppose t₁ Theorem transitions visits