## 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 90

Page 64

It is well known that the scalar differential equation dz(t) dt = az(t) has the

2(t) = 2(0)e". This suggests that the

) = P(0)e^* = e^* (2.41) If we introduce the matrix series ea = $ 4" 40 – 1 n = 0 ...

It is well known that the scalar differential equation dz(t) dt = az(t) has the

**solution**2(t) = 2(0)e". This suggests that the

**solution**of (2.40) can be written in the form P(t) = P(0)e^* = e^* (2.41) If we introduce the matrix series ea = $ 4" 40 – 1 n = 0 ...

Page 138

Application of the Laplace transform to the Kolmogorov diffusion equations

removes the time variable t (or T), leaving an ordinary differential equation the

a ...

Application of the Laplace transform to the Kolmogorov diffusion equations

removes the time variable t (or T), leaving an ordinary differential equation the

**solution**of which yields the transform of the probability distribution (or density) asa ...

Page 216

This general system, however, is not of great interest in the study of gene

frequencies in the case of random drift, since the general

an interpretation which is biologically meaningful. We are primarily interested in

the ...

This general system, however, is not of great interest in the study of gene

frequencies in the case of random drift, since the general

**solution**does not admitan interpretation which is biologically meaningful. We are primarily interested in

the ...

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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