## 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

For the birth and birth-and-death processes the problems of uniqueness are

considered. In some cases we use several methods to obtain a solution to the

differential-difference equation,1 our main purpose being to illustrate the various

methods that are available for treating stochastic differential-difference equations.

B. The

discontinuous Markov' processes. This process occupies a unique position in the

theory of probability ...

For the birth and birth-and-death processes the problems of uniqueness are

considered. In some cases we use several methods to obtain a solution to the

differential-difference equation,1 our main purpose being to illustrate the various

methods that are available for treating stochastic differential-difference equations.

B. The

**Poisson Process**. The**Poisson process**is the simplest of thediscontinuous Markov' processes. This process occupies a unique position in the

theory of probability ...

Page 76

Hence 22{X(t)} = (At)2 + At - (A*)1 = At (2.95) We find, then, that for the

function Px(t), which has been interpreted as the probability that exactly x

changes have taken place in an interval of length t. Let us now consider the

transition probabilities Pit(t) associated with the

of Sec. 2.2 and the assumptions for the

intensities g, and the ...

Hence 22{X(t)} = (At)2 + At - (A*)1 = At (2.95) We find, then, that for the

**Poisson****process**the mean and variance are equal. Thus far we have considered only thefunction Px(t), which has been interpreted as the probability that exactly x

changes have taken place in an interval of length t. Let us now consider the

transition probabilities Pit(t) associated with the

**Poisson process**. From the theoryof Sec. 2.2 and the assumptions for the

**Poisson process**, we see that theintensities g, and the ...

Page 248

Albert T. Bharucha-Reid. In order to compare the two models considered thus far,

we consider the relative fluctuation or coefficient of variation, the relative

fluctuation being defined as the ratio For the

model) we obtain nt) = WT1 (5.42) and for the Furry model we obtain -T(t) = [1 - e-

"]1 ~ 1 (5.43) where U is not too small. On comparing (5.42) and (5.43) we see

that the relative fluctuation for the Furry distribution is much larger than the

relative fluctuation ...

Albert T. Bharucha-Reid. In order to compare the two models considered thus far,

we consider the relative fluctuation or coefficient of variation, the relative

fluctuation being defined as the ratio For the

**Poisson process**(Bhabha-Heitlermodel) we obtain nt) = WT1 (5.42) and for the Furry model we obtain -T(t) = [1 - e-

"]1 ~ 1 (5.43) where U is not too small. On comparing (5.42) and (5.43) we see

that the relative fluctuation for the Furry distribution is much larger than the

relative fluctuation ...

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### Contents

Preface | 1 |

Processes Continuous In Space and Time | 3 |

Processes Discrete in Space and Time | 9 |

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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