## Introduction to Stochastic ProcessesProbability spaces and random variables. Expectations and independence. Bernoulli processes and sums of independent random variables. Poisson processes. Markov chains. Limiting Behavior and applications of Markov chains. Potentials, excessive functions, and optimal stopping of Markov chains. Markov processes. Renewal theory. Markov renewal theory. Non-negative matrices. |

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### Contents

Preface | 1 |

Expectations and Independence | 21 |

Bernoulli Processes | 43 |

Copyright | |

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applies arrivals becomes bounded called Chapter closed completes Compute conditional Consider constant continuous convergence Corollary corresponding customers defined definition denote depends discrete distribution eigenvalue equal equation event EXAMPLE excessive Exercise exists expected value exponential fact failure Figure Find finite fixed function function f given gives Hence holds implies independent infinite initial integral interested interval irreducible jumps lifetime limit limiting distribution Markov chain Markov process mean measure non-negative observe obtain occurs optimal stopping otherwise parameter particular payoff period Poisson process positive possible preceding probability problem Proof Proposition queue random variable reached recurrent remaining replaced respective result Riemann integrable satisfies sequence solution space starting successive Suppose taking term Theorem theory tion transient transition matrix units visits write