Homogeneous Denumerable Markov Processes [Paperback]

Markov 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.Markov 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.I Construction Theory of Sample Functions of Homogeneous Denumerable Markov Processes.- I The First Construction Theorem.- ? 1.1 Introduction.- ? 1.2 Definition of transformation gn.- ? 1.3 Convergence of the sequence X(n)(?) (n?1).- ? 1.4 Further properties of X(n)(?) (n?1).- ? 1.5 The first construction theorem.- II The Second Construction Theorem.- ? 2.1 Introduction.- ? 2.2 The mapping Tmn.- ? 2.3 The mapping Wn.- ? 2.4 Constructing auxiliary functions.- ? 2.5 The second construction theorem.- ? 2.6 Summary.- ? 2.7 Two notes.- II Theory of Minil32