## Homogeneous Denumerable Markov ProcessesMarkov processes play an important role in the study of probability theory. Homogeneous denumerable Markov processes are among the main topics in the theory and have a wide range of application in various fields of science and technology (for example, in physics, cybernetics, queuing theory and dynamical programming). This book is a detailed presentation and summary of the research results obtained by the authors in recent years. Most of the results are published for the first time. Two new methods are given: one is the minimal nonnegative solution, the second the limit transition method. With the help of these two methods, the authors solve many important problems in the framework of denumerable Markov processes. |

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### Contents

Chapter | 3 |

Criteria for the Uniqueness of QProcesses | 12 |

The Second Construction Theorem | 16 |

Copyright | |

14 other sections not shown

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### Common terms and phrases

1-bounded equations atomic almost closed Av(i boundary theory called Cauchy sequence chapter closed set construction theorem Corollary cºx deduce defined Definition denote determined uniquely distribution and moments excessive function exist infinitely F-type Q-process first-type system flying point harmonic function Hence holds homogeneous denumerable Markov ie Dº ie E ie/E II(a II(b je E ke|E Markov chain Markov process Markov property matrix of order minimal nonnegative solution minimal Q-process necessary and sufficient nonnegative linear equations normal system oeſ probability space proof of Theorem pseudo-normal system Q is conservative Q is nonconservative Q-process is unique Q-process of order random variable second-type ſº strictly nonhomogeneous equations sufficient condition system of 1-bounded system of equations system of homogeneous system of nonnegative system of strictly teſ0 transition probability matrix unique ordinary zero solution

### References to this book

Continuous-time Markov Chains and Applications: A Singular Perturbation Approach George Yin,Qing Zhang No preview available - 1998 |

Markov Processes and Controlled Markov Chains Zhenting Hou,Jerzy A. Filar,Anyue Chen Limited preview - 2002 |