## 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 309

Let the random variable Zr represent the distance between the time T and the

time of

most a impulses

observe ...

Let the random variable Zr represent the distance between the time T and the

time of

**arrival**of the next impulse—if the counter is free. Now, the probability of atmost a impulses

**arriving**in the interval (T, T + t) is 1 – 3%(Zr s t)*.G.(t)}. Weobserve ...

Page 375

If the server is busy with another customer, the newly

until the server is free. In the meantime other customers may

If customers

If the server is busy with another customer, the newly

**arrived**customer must waituntil the server is free. In the meantime other customers may

**arrive**at the service.If customers

**arrive**when the server is busy, they must form a queue or waiting ...Page 397

B. Equilibrium Theory for Telephone Exchanges with an Infinite and Finite

Number of Channels. The Markovian Case: Negative-exponential

Holding Times. In this section we consider the equilibrium theory for telephone

exchanges ...

B. Equilibrium Theory for Telephone Exchanges with an Infinite and Finite

Number of Channels. The Markovian Case: Negative-exponential

**Arrival**andHolding Times. In this section we consider the equilibrium theory for telephone

exchanges ...

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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