## 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 73

(1) The probability of a change in the interval (t, t + At) is A At + o(A<), where A is

a positive constant ... In view of the above assumptions, we are led to the

following relation for

This ...

(1) The probability of a change in the interval (t, t + At) is A At + o(A<), where A is

a positive constant ... In view of the above assumptions, we are led to the

following relation for

**Px**(**t**+ At):**Px**(**t**+ At) = (1 - A At)**Px**(**t**) + XP^t) At + o(At) (2.83)This ...

Page 96

Now P{X(t) = X\T} = fqn\ I Ptl{t - r) • • • Ptm(t - t)] n=»0 W,-) H»=a ' where the term in

braces is the coefficient of a* in the expansion of i

reasoning used above is the same as that used in the theory of compound ...

Now P{X(t) = X\T} = fqn\ I Ptl{t - r) • • • Ptm(t - t)] n=»0 W,-) H»=a ' where the term in

braces is the coefficient of a* in the expansion of i

**px**(**t**- t)«* 7 = F»{3, t - t) (Thereasoning used above is the same as that used in the theory of compound ...

Page 441

Proof: The distribution of Y(t) is the convolution of

Fx(a,t) and -F2(5>0 gives the product G(s,t). On collecting terms, we see that the ...

Proof: The distribution of Y(t) is the convolution of

**Px**(**t**) and Qx(t), that is, Rv(t) =**Px**(**t**)*Qx(t) = £ PmQy-i(t) (A.7) «=o Termwise multiplication of the power series forFx(a,t) and -F2(5>0 gives the product G(s,t). On collecting terms, we see that the ...

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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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