## Elements of the theory of Markov processes and their applicationsGraduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition. |

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Page 10

the

processes and branchingprocesses. Finally, inSec. 1.8, we consider IV-

dimensional processes, i.e., processes in which the population is made up of N

different ...

the

**nonnegative**integers and discuss the relationship between random- walkprocesses and branchingprocesses. Finally, inSec. 1.8, we consider IV-

dimensional processes, i.e., processes in which the population is made up of N

different ...

Page 25

C. Proof of the Fundamental Theorem (fixed-point method).1 CO The generating

function F(s) = 2 p(x)s" is a power series in s whose coefficients, being

probabilities, are all

, F(s) is ...

C. Proof of the Fundamental Theorem (fixed-point method).1 CO The generating

function F(s) = 2 p(x)s" is a power series in s whose coefficients, being

probabilities, are all

**nonnegative**. In addition, .P(O) = p(0) > 0 and F(l) = 1 ; hence, F(s) is ...

Page 44

If the Markov matrix P = (pit) is given, we can study the properties of the motion of

the particle.1 The interpretation of a simple discrete branching process as a

random walk on the

particle ...

If the Markov matrix P = (pit) is given, we can study the properties of the motion of

the particle.1 The interpretation of a simple discrete branching process as a

random walk on the

**nonnegative**integers 0, 1, 2, ... is as follows: At t = 0 the "particle ...

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### Contents

Introduction | 1 |

Processes Discrete in Space and Time | 9 |

Processes Discrete in Space and Continuous in Time | 57 |

Copyright | |

10 other sections not shown

### Other editions - View all

Elements of the Theory of Markov Processes and Their Applications A. T. Bharucha-Reid Limited preview - 2012 |

Elements of the Theory of Markov Processes and Their Applications Albert T. Bharucha-Reid Limited preview - 1997 |

### Common terms and phrases

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