## 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. |

### From inside the book

Results 1-3 of 37

Page 248

In order to compare the two models considered thus far, we consider the relative

ratio 2(X(t)} % (t) = ++! (5.41) &{X(t)} For the Poisson process (Bhabha-Heitler ...

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 theratio 2(X(t)} % (t) = ++! (5.41) &{X(t)} For the Poisson process (Bhabha-Heitler ...

Page 292

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 Messel, H.:

Further Results on the

and the Probability Distribution Function, Proc. Phys. Soc. (London), ser. A, vol.

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 Messel, H.:

Further Results on the

**Fluctuation**Problem in ElectronPhoton Cascade Theoryand the Probability Distribution Function, Proc. Phys. Soc. (London), ser. A, vol.

Page 465

... 40 Discrete process, diffusion equation representation of, 154–158 Dishonest

processes, 71m., 81, 92 Dissipative chain, 34 Ehrenfest process, 122 Electron-

photon cascade, 235

process, ...

... 40 Discrete process, diffusion equation representation of, 154–158 Dishonest

processes, 71m., 81, 92 Dissipative chain, 34 Ehrenfest process, 122 Electron-

photon cascade, 235

**fluctuation**problem for, 246—265 Elementary returnprocess, ...

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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