## 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 2

We

population can only increase in size and that the increase in the interval (t, t + At)

is proportional to the number of bacteria present at time t. Hence, we have the ...

We

**assume**(1) that at time t there are a bacteria in the population and (2) that thepopulation can only increase in size and that the increase in the interval (t, t + At)

is proportional to the number of bacteria present at time t. Hence, we have the ...

Page 48

In the one-dimensional case the random variables X,

space 3: which consisted of the nonnegative integers; in the N-dimensional case,

however, the state space 3 is the N-dimensional Euclidean space. Since the ...

In the one-dimensional case the random variables X,

**assumed**values in the statespace 3: which consisted of the nonnegative integers; in the N-dimensional case,

however, the state space 3 is the N-dimensional Euclidean space. Since the ...

Page 390

The expression for the Laplace-Stieltjes transform of F*(w) is equivalent to the

solution obtained by Khintchine [41]. If, following Khintchine, we

Au < 1 the limiting distribution function F*(w) exists, then Eq. (9.38) can be

obtained ...

The expression for the Laplace-Stieltjes transform of F*(w) is equivalent to the

solution obtained by Khintchine [41]. If, following Khintchine, we

**assume**that forAu < 1 the limiting distribution function F*(w) exists, then Eq. (9.38) can be

obtained ...

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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