## 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 44

A random walk is the motion along a line executed by a

unit time, can move one unit to the right, move one unit to the left, or stand still,

the probabilities of these transitions depending in general on the position of the ...

A random walk is the motion along a line executed by a

**particle**which, at eachunit time, can move one unit to the right, move one unit to the left, or stand still,

the probabilities of these transitions depending in general on the position of the ...

Page 257

0 is the probability that a primary

the interval (t, t + dt) giving rise to secondary

E '+ dB") and (E", E" + dE"). It is now assumed that w(e',e") = 0 for e' + e" > 1, ...

0 is the probability that a primary

**particle**of energy Eo experiences a collision inthe interval (t, t + dt) giving rise to secondary

**particles**in the energy intervals (E",E '+ dB") and (E", E" + dE"). It is now assumed that w(e',e") = 0 for e' + e" > 1, ...

Page 284

... E:t) denote the product densities of degree 1 for electrons and photons,

respectively, where the subscript i = 1 if the cascade is initiated by an electron

and i = 2 if the cascade is initiated by a photon, the initiating

energy Eo.

... E:t) denote the product densities of degree 1 for electrons and photons,

respectively, where the subscript i = 1 if the cascade is initiated by an electron

and i = 2 if the cascade is initiated by a photon, the initiating

**particle**havingenergy Eo.

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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