## 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 42

Page 12

B. Transition Probabilities and Markov

terminology of Markov chain theory, we call the conditional probability p, the

probability of a transition from the state i to the state j, and call P = (pg) the

of ...

B. Transition Probabilities and Markov

**Matrices**. In order to conform with theterminology of Markov chain theory, we call the conditional probability p, the

probability of a transition from the state i to the state j, and call P = (pg) the

**matrix**of ...

Page 14

The Markov

form of a partitioned

represent Markov

sets of ...

The Markov

**matrix**associated with a decomposable chain can be written in theform of a partitioned

**matrix**; for example, p- . 0 P. In the above, P, and P,represent Markov

**matrices**which describe the transitions within the two closedsets of ...

Page 35

We now give two limit theorems, due to Foster, associated with what has been

termed a generalized discrete branching process. This process is described by a

Markov

...

We now give two limit theorems, due to Foster, associated with what has been

termed a generalized discrete branching process. This process is described by a

Markov

**matrix**P = (p,) with the following properties: (a) pig > 0 X pu = 1 i = 0, 1, 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