## 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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Results 1-3 of 83

Page 250

in the

E:t) dB + 0(dE)*] P, e O(dE)” n > 1 Hence, we assume that the probability of ...

in the

**interval**dB. If we now denote by P, the probability that n particles are in the**interval**dB, then P, ef,(E:t) dB + O(dE)* = &{dx(E:t)} + O(dE)” Po = 1 – P1 = 1 — [f(E:t) dB + 0(dE)*] P, e O(dE)” n > 1 Hence, we assume that the probability of ...

Page 283

with energy greater than E, at the time of its production (E, is called the primitive

energy), are produced by a single particle of type i with energy Eo in the

0,t). It has been suggested that this function has more elegant mathematical ...

with energy greater than E, at the time of its production (E, is called the primitive

energy), are produced by a single particle of type i with energy Eo in the

**interval**(0,t). It has been suggested that this function has more elegant mathematical ...

Page 285

The two electrons, one electron produced in the

produced in the

depth ti. 2. The two electrons have two different ancestors at depth ti.

The two electrons, one electron produced in the

**interval**(t1, t, + dti) and the otherproduced in the

**interval**(ta, to + dtz), where to > ti, have a common ancestor atdepth ti. 2. The two electrons have two different ancestors at depth ti.

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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