## 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

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Page 12

B.

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 matrix

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 63

(t) and Q,(t), we call a,(t) At + os At) the infinitesimal

Markov process {X(t), t > 0}." If we now put P(t) = (P,(t)), the Kolmogorov equations

can be written in the form dP(t) # = P040 (2.35) dP(t) A(t) P(t) (2.36) dt with P(0) ...

(t) and Q,(t), we call a,(t) At + os At) the infinitesimal

**transition probabilities**of theMarkov process {X(t), t > 0}." If we now put P(t) = (P,(t)), the Kolmogorov equations

can be written in the form dP(t) # = P040 (2.35) dP(t) A(t) P(t) (2.36) dt with P(0) ...

Page 103

is a stationary Markov chain with

the matrix of

chain defined by the above

is a stationary Markov chain with

**transition probabilities**p?' = P,(nt) and, for n = 1,the matrix of

**transition probabilities**P = (Pd(r)), i,j = 0, 1, ... for any one r > 0. Thechain defined by the above

**transition probabilities**is aperiodic, since Pit(nt) > 0, ...### 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