## 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 253

As we would expect, the integrodifferential equations for the product

functions of degree 1 are the same as the equations obtained by Landau and

Rumer for Approximation A and by Bhabha and Chakrabarty for Approximation B.

In ...

As we would expect, the integrodifferential equations for the product

**density**functions of degree 1 are the same as the equations obtained by Landau and

Rumer for Approximation A and by Bhabha and Chakrabarty for Approximation B.

In ...

Page 283

We now define the product

theory, and in the next section we derive the integral equations which the product

E.

We now define the product

**density**functions in the Ramakrishnan-Srinivasantheory, and in the next section we derive the integral equations which the product

**density**functions satisfy in the case of an electron-photon cascade. Let F,(E1, ...,E.

Page 342

It is important to note that regardless of how large y may be, the

positions t and t' are not independent for T in the interval (0, 1|y). This property of

the Markovian

It is important to note that regardless of how large y may be, the

**densities**at thepositions t and t' are not independent for T in the interval (0, 1|y). This property of

the Markovian

**density**field is of great interest in astrophysical applications, for it ...### 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