## 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 73

In order to derive the differential equation, it is necessary to state the

which specify the manner in which the Poisson process develops.

for the Poisson Process. (1) The probability of a change in the interval (t, t + At) ...

In order to derive the differential equation, it is necessary to state the

**assumptions**which specify the manner in which the Poisson process develops.

**Assumptions**for the Poisson Process. (1) The probability of a change in the interval (t, t + At) ...

Page 85

We now define and investigate a process which can be termed a death process.

In this case the random variable X(t) is a strictly decreasing function of time.

, i.e., ...

We now define and investigate a process which can be termed a death process.

In this case the random variable X(t) is a strictly decreasing function of time.

**Assumptions**for the Death Process. (1) At time zero the system is in a state z = zo, i.e., ...

Page 176

Because of the above

growth of sexes here considered is a bivariate process of the birth-and-death

type. It is clear from the above

Because of the above

**assumptions**, we see that the stochastic process for thegrowth of sexes here considered is a bivariate process of the birth-and-death

type. It is clear from the above

**assumptions**that the probabilities P.,(t) satisfy the ...### What people are saying - Write a review

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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