## 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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Results 1-3 of 83

Page 29

The satisfy the equations "i = Z"iPtl [1-60] <=o with = I. and the distribution {77 1}

is uniquely determined. i-o Proof: By hypothesis, the states j have finite mean

recurrence times Ms. Let 7r, = Mf1. Nowpj"} —>□ n,;

= j.

The satisfy the equations "i = Z"iPtl [1-60] <=o with = I. and the distribution {77 1}

is uniquely determined. i-o Proof: By hypothesis, the states j have finite mean

recurrence times Ms. Let 7r, = Mf1. Nowpj"} —>□ n,;

**hence**, (1.61) holds for 00 *= j.

Page 84

Similar calculations for the second moment give (1 + a)m'(f) + m(f) = (1 + a)(A<)2

+ Xt

a linear function of time and the variance is a quadratic function of time. We now ...

Similar calculations for the second moment give (1 + a)m'(f) + m(f) = (1 + a)(A<)2

+ Xt

**hence**&{X(t)} = Xt(l + <xM) (2.128)**Hence**, for the P61ya process the mean isa linear function of time and the variance is a quadratic function of time. We now ...

Page 250

If we now denote by Pn the probability that n particles are in the interval dE, then

= f1(E,t) dE + 0(dEf = S{dX(E;t)} + 0(dEf P0 = 1 - Px = 1 - VXW) dE + 0(dEf) Pn = 0(

dE)n n > 1

If we now denote by Pn the probability that n particles are in the interval dE, then

= f1(E,t) dE + 0(dEf = S{dX(E;t)} + 0(dEf P0 = 1 - Px = 1 - VXW) dE + 0(dEf) Pn = 0(

dE)n n > 1

**Hence**, we assume that the probability of having one particle in the ...### What people are saying - Write a review

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### Contents

Introduction | 1 |

Processes Discrete in Space and Time | 9 |

Processes Discrete in Space and Continuous in Time | 57 |

Copyright | |

10 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 |

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