## 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 48

Page 12

... P12 P20 P21 P22 Clearly P is a square matriæ (of infinite order since the chain

has a denumerable number of states) with nonnegative elements, since pu - 0

CO for all i and j, and with row sums

... P12 P20 P21 P22 Clearly P is a square matriæ (of infinite order since the chain

has a denumerable number of states) with nonnegative elements, since pu - 0

CO for all i and j, and with row sums

**equal**to unity, since X. ply = 1 j = 0 for all i.Page 101

When transformation takes place, the following may occur: (1) The individual can

die with probability qo(r), where qo(r) is an increasing function of r that is

1 — B when r = 0 and

When transformation takes place, the following may occur: (1) The individual can

die with probability qo(r), where qo(r) is an increasing function of r that is

**equal**to1 — B when r = 0 and

**equal**to unity when r = ob. (2) The individual can be ...Page 226

(4.184) From (4.184) we see that, for small values of time, log X,(t) plotted against

log tis a straight line whose slope is

intercept on the ordinate is the geometric average of the intensities of damage A."

.

(4.184) From (4.184) we see that, for small values of time, log X,(t) plotted against

log tis a straight line whose slope is

**equal**to the number of states n and theintercept on the ordinate is the geometric average of the intensities of damage A."

.

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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