## 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 49

As in the one-dimensional case, we can obtain the

differentiation of the generating function. In this case we define m!” = o (1.123 ij

0s, s1=s* = . . . = sw-1 - ) as the expected number of individuals of type j (j = 1, 2, ..

., N) in the ...

As in the one-dimensional case, we can obtain the

**moments**of X, bydifferentiation of the generating function. In this case we define m!” = o (1.123 ij

0s, s1=s* = . . . = sw-1 - ) as the expected number of individuals of type j (j = 1, 2, ..

., N) in the ...

Page 97

After solving integral equation (2.178) for ma(t), the variance of X(t) can be

obtained, since 2*{X(t)} = m2(t) + m1(t) — [m](t)]”. It is of interest to note that the

equations for the

because ...

After solving integral equation (2.178) for ma(t), the variance of X(t) can be

obtained, since 2*{X(t)} = m2(t) + m1(t) — [m](t)]”. It is of interest to note that the

equations for the

**moments**are integral equations of the renewal type, so calledbecause ...

Page 273

Hence, from (5.123) and (5.125), the kth factorial

K. Y.(s1, ..., so p) (5.127) 2. The Jánossy G-Equations. In Sec. 5.2C the Jánossy G

-equations were derived for both nucleon and electron-photon cascades.

Hence, from (5.123) and (5.125), the kth factorial

**moment**is given by T.(Bo;E:t) =K. Y.(s1, ..., so p) (5.127) 2. The Jánossy G-Equations. In Sec. 5.2C the Jánossy G

-equations were derived for both nucleon and electron-photon cascades.

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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