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Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of

Markov processes --- Stochastic processes --- Markov, Processus de --- Processus stochastiques --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Markov processes. --- Stochastic processes. --- Random processes --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Probabilities

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The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other.The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processe

Stochastic processes --- 519.216 --- 519.2 --- Random processes --- Probabilities --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Stochastic Processes --- Processus stochastiques --- Stochastic Processes. --- Stochastic processes. --- Probabilités. --- Markov, Processus de --- Markov processes --- Probabilités.

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From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zürich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal…The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews) This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text.

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This book provides a rigorous, comprehensive introduction to the finite Markov chain imbedding technique for studying the distributions of runs and patterns from a unified and intuitive viewpoint, away from the lines of traditional combinatorics. The central theme of this approach is to properly imbed the random variables of interest into the framework of a finite Markov chain, and the resulting representations of the underlying distributions are compact and very amenable to further study of associated properties. The concept of finite Markov chain imbedding is systematically developed, and i

Markov processes. --- Random variables. --- Distribution (Probability theory) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Chance variables --- Stochastic variables --- Variables (Mathematics) --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Markov, Processus de --- Variables aléatoires --- Distribution (Théorie des probabilités)

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In this book, the functional inequalities are introduced to describe:(i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;(ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;(iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.

Ordered algebraic structures --- Stochastic processes --- Inequalities (Mathematics) --- Semigroups of operators. --- Dirichlet forms --- Markov processes --- Spectral theory (Mathematics) --- Inégalités (Mathématiques) --- Semi-groupes d'opérateurs --- Dirichlet, Formes de --- Markov, Processus de --- Spectre (Mathématiques) --- ELSEVIER-B EPUB-LIV-FT --- Semigroups. --- Markov processes. --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Group theory --- Processes, Infinite