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. |
Contents
Chapter II | 16 |
Part II | 29 |
Calculation | 41 |
Chapter V | 47 |
6 | 53 |
8 | 61 |
Martin Exit Boundary Theory | 93 |
5 | 99 |
Martin Entrance Boundary Theory | 124 |
Minimal QProcesses | 133 |
7 | 166 |
Arbitrary QProcesses | 186 |
Construction Theory of Homogeneous Denumerable | 200 |
Construction of QProcesses | 240 |
Qualitative Theory | 246 |
| 279 | |
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Common terms and phrases
atomic almost closed ax)e blockable random Cauchy sequence closed set Corollary deduce defined Definition denote Denumerable Markov Processes determined uniquely distribution and moments E₁ excessive function excessive measure exist infinitely F-type Q-process finite first-type system harmonic function Hence holds homogeneous denumerable Markov ie E iɛE II(b je E k&A H Lemma Markov chain Markov property matrix of order minimal nonnegative solution minimal Q-process N-BF-type necessary and sufficient nonnegative linear equations P₁ Pij(t Pmin probability space proof of Theorem pseudo-normal system Q is conservative Q is nonconservative Q-matrix is given Q-process is unique Q-process of order qi qi random system random variable recurrent second-type strictly nonhomogeneous equations sufficient condition Suppose a Q-matrix system of 1-bounded system of equations system of nonnegative system of strictly t₁ Theorem unique ordinary zero solution