## 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 182

The probability of a unit increase in the population size of S, in the interval (t, t +

At),

probability of a unit decrease in the population size of S, in the interval (t, t + At), ...

The probability of a unit increase in the population size of S, in the interval (t, t +

At),

**given**that there are exactly a individuals in Si at time t, is A, At + O(At). 2. Theprobability of a unit decrease in the population size of S, in the interval (t, t + At), ...

Page 269

dB, denote the differential probability that after a depth t a primary nucleon of

energy Eo has

), i = 1, 2, ..., n. Messel and Potts have shown that H,(Eo; E1, ..., E.; t) satisfies the

...

dB, denote the differential probability that after a depth t a primary nucleon of

energy Eo has

**given**rise to n nucleons with energies in the intervals (E, E, -i- d.E.), i = 1, 2, ..., n. Messel and Potts have shown that H,(Eo; E1, ..., E.; t) satisfies the

...

Page 354

Here p,(t) is the probability that a photon absorbed at a

reemitted in a

atmosphere. C. The H-Equation. The Law of Darkening. For a diffuse radiation

field, i.e. ...

Here p,(t) is the probability that a photon absorbed at a

**given**point t will bereemitted in a

**given**direction u in the radiation emerging from the surface of theatmosphere. C. The H-Equation. The Law of Darkening. For a diffuse radiation

field, i.e. ...

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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