## A First Course in Stochastic ProcessesThe purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other. The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory. |

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### Contents

1 | |

Chapter 2 MARKOV CHAINS | 45 |

Chapter 3 THE BASIC LIMIT THEOREM OF MARKOV CHAINS AND APPLICATIONS | 81 |

Chapter 4 CLASSICAL EXAMPLES OF CONTINUOUS TIME MARKOV CHAINS | 117 |

Chapter 5 RENEWAL PROCESSES | 167 |

Chapter 6 MARTINGALES | 238 |

### Other editions - View all

A First Course in Stochastic Processes, Volume 1 Samuel Karlin,Howard M. Taylor Limited preview - 1975 |

### Common terms and phrases

a-field arbitrary assume birth and death bounded branching process Brownian motion process Chapter compute Consider constant continuous covariance function covariance stationary process death process defined definition denote determine distributed random variables distribution function distribution with parameter E[Xo E[XT eigenvalue event example exponential distribution finite fixed follows formula Gaussian given Hence Hint implies independent random variables inequality integer interval joint distribution law of total Lemma Let X(t limit linear Markov chain Markov process Markov property martingale martingale with respect mean square error nonnegative normal distribution obtain particle Poisson process population positive Pr(X Pr{T Pr{X Pr{Y predictor probability generating function process X(t proof prove queueing random walk real numbers recurrent renewal equation renewal process sample satisfying Section sequence Show solution stationary process stochastic process submartingale supermartingale Suppose theory total probability transition probability matrix variance vector verify zero mean