## 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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Results 1-3 of 73

Page 61

We now turn from the general form of Eqs. (2.19) and (2.20) and consider a

specialized form which is of

in which the random variable X(t) can only assume a denumerable number of

values, ...

We now turn from the general form of Eqs. (2.19) and (2.20) and consider a

specialized form which is of

**interest**in many applications. We consider the casein which the random variable X(t) can only assume a denumerable number of

values, ...

Page 139

The processes, which are of great

illustrate the methods of solving diffusion equations outlined in Sec. 3.2E. 1. The

Wiener-Lévy Process: The Heat Equation. The differential equation ôu = D 3°u w

= u(t ...

The processes, which are of great

**interest**in their own right, will be used toillustrate the methods of solving diffusion equations outlined in Sec. 3.2E. 1. The

Wiener-Lévy Process: The Heat Equation. The differential equation ôu = D 3°u w

= u(t ...

Page 199

Of particular

with a finite or denumerable number of states. It is of

paper on stochastic epidemics seems to have been published by McKendrick [72

] ...

Of particular

**interest**in the stochastic theory of epidemics are Markov processeswith a finite or denumerable number of states. It is of

**interest**to note that the firstpaper on stochastic epidemics seems to have been published by McKendrick [72

] ...

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### Contents

Introduction | 1 |

Processes Discrete in Space and Continuous in Time | 57 |

Processes Continuous in Space and Time | 129 |

Copyright | |

9 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

absorber addition applications approach arrival associated assume assumptions becomes birth boundary branching processes called cascade coefficients collision concerned condition consider constant continuous counter death defined denote density derive described determined developed differential equation diffusion discussion distribution function electron energy epidemic equal exists expected expression finite fluctuation given gives growth Hence independent individuals initial condition integral interest interval introduce Kolmogorov equations Laplace transform length limit machine Markov Markov chain Markov processes Math mathematical mean method moments necessary nucleon obtain particle particular photon Poisson population positive primary problem Proof properties queueing radiation random variable reaction refer relation represent respectively satisfies shown simple ſº solution Statist Stochastic Processes Theorem theory tion transition probabilities zero