## 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 74

Page 19

statistically

that pu = coefficient of s” in [F(s)] (1.29) In order to determine the n-step transition

probabilities, we need the following theorem. Theorem 1.2: The generating ...

statistically

**independent**, it follows from the definition of the generating functionthat pu = coefficient of s” in [F(s)] (1.29) In order to determine the n-step transition

probabilities, we need the following theorem. Theorem 1.2: The generating ...

Page 396

are identically distributed

are

function of the holding times is negative-exponential, i.e., B(S) = 1 – e's for 5 - 0 =

0 for ...

are identically distributed

**independent**positive random variables and that theyare

**independent**of the process (T,). It is further assumed that the distributionfunction of the holding times is negative-exponential, i.e., B(S) = 1 – e's for 5 - 0 =

0 for ...

Page 424

Since the $, t, and 2,nt, are

becomes 2. +2-tonri S ac 2*n- - o - * +3*, *. i = 1 3-,-] - * +3*, *.) i = 1 i = 1 where

the service times $1, . . . , ś, are

Since the $, t, and 2,nt, are

**independent**, the conditional probability in (9.158)becomes 2. +2-tonri S ac 2*n- - o - * +3*, *. i = 1 3-,-] - * +3*, *.) i = 1 i = 1 where

the service times $1, . . . , ś, are

**independent**and identically distributed random ...### What people are saying - Write a review

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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