## 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 138

We now consider the application of the

Kolmogorov diffusion equations. Again we consider the forward Kolmogorov

equation, the procedure being the same for the backward equation. Application

of the Laplace ...

We now consider the application of the

**Laplace transformation**" to theKolmogorov diffusion equations. Again we consider the forward Kolmogorov

equation, the procedure being the same for the backward equation. Application

of the Laplace ...

Page 149

In this section we obtain the

distribution. Thus, with the

inversion theorem yields the firstpassage time distribution. We first show that the

Laplace ...

In this section we obtain the

**Laplace transform**of the first-passage timedistribution. Thus, with the

**Laplace transform**obtained, an application of theinversion theorem yields the firstpassage time distribution. We first show that the

Laplace ...

Page 444

B. The Laplace-Stieltjes Transform and the

Stieltjes Transform. If F(t) is a complex function of the real variable t for 0 < t < oo

and if F(t) is of bounded variation in any closed interval [0, u] of the positive real ...

B. The Laplace-Stieltjes Transform and the

**Laplace Transform**. 1. The Laplace-Stieltjes Transform. If F(t) is a complex function of the real variable t for 0 < t < oo

and if F(t) is of bounded variation in any closed interval [0, u] of the positive real ...

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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