## 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 143

In these cases no

are called natural. Second, the coefficients may be such that X(t) has positive

probability of taking the value r, or ra. For these processes there are two possible

...

In these cases no

**boundary**conditions have to be imposed, and the boundariesare called natural. Second, the coefficients may be such that X(t) has positive

probability of taking the value r, or ra. For these processes there are two possible

...

Page 144

The

all other cases the

above criteria, we consider the classification of the boundaries associated with a

...

The

**boundary**r, is an entrance**boundary**if g(x) e L(II) and wosso do e Lu). 4. Inall other cases the

**boundary**is called natural. To illustrate the application of theabove criteria, we consider the classification of the boundaries associated with a

...

Page 145

When ri, say, is a natural

problem for the backward diffusion equation has infinitely many solutions, but that

for the forward diffusion equation is uniquely determined. 5. When ri is a natural ...

When ri, say, is a natural

**boundary**and rais an exit**boundary**, the initial valueproblem for the backward diffusion equation has infinitely many solutions, but that

for the forward diffusion equation is uniquely determined. 5. When ri is a natural ...

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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