## 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 154

2 we saw that the discontinuous Markov processes could be considered as

random-walk processes depending on a continuous time parameter. In this

section we wish to consider the relationship between the generating-function

2 we saw that the discontinuous Markov processes could be considered as

random-walk processes depending on a continuous time parameter. In this

section we wish to consider the relationship between the generating-function

**approach**of ...Page 168

Early studies in the mathematical theory of population growth were primarily

concerned with the development of deterministic models of the macro type. In this

number ...

Early studies in the mathematical theory of population growth were primarily

concerned with the development of deterministic models of the macro type. In this

**approach**a functional equation (differential or integral equation, etc.) for thenumber ...

Page 287

D. Other Studies Based on the New

99] have given numerical calculations of the mean number of electrons in a

cascade with energies greater than E at depth t. In particular, they have obtained

the ...

D. Other Studies Based on the New

**Approach**. 1. Srinivasan and Ranganathan [99] have given numerical calculations of the mean number of electrons in a

cascade with energies greater than E at depth t. In particular, they have obtained

the ...

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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