## 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 61

Page 103

The chain defined by the above transition probabilities is aperiodic, since Pit(nt) >

0, and, therefore, lim P.,(nt)

continuity of the transition probabilities for i and j fixed, it follows that this limit is ...

The chain defined by the above transition probabilities is aperiodic, since Pit(nt) >

0, and, therefore, lim P.,(nt)

**exists**for each fixed r > 0. Now, from the uniformcontinuity of the transition probabilities for i and j fixed, it follows that this limit is ...

Page 395

distribution of waiting times

lim F,(t) = F(t)

Theorem 9.10: A necessary and sufficient condition that lim F,(t) = F(t)

that ...

distribution of waiting times

**exists**; i.e., when does the limiting distribution functionlim F,(t) = F(t)

**exist**? This question is answered by pa-- the following theorem.Theorem 9.10: A necessary and sufficient condition that lim F,(t) = F(t)

**exists**isthat ...

Page 444

e-*d F(t) (B.5) w—-oo o'0 0.

integral (B.4) converges for A = A*. It can be shown that there

of convergence A, with the property that the integral (B.5) converges if 3(A) > 2, ...

e-*d F(t) (B.5) w—-oo o'0 0.

**exists**for a certain value of A, say A*, we say that theintegral (B.4) converges for A = A*. It can be shown that there

**exists**an abscissaof convergence A, with the property that the integral (B.5) converges if 3(A) > 2, ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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