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Probability theory has grown from a modest study of simple games of change to a subject with application in almost every branch of knowledge and science. In this exciting book, a number of distinguished probabilists discuss their current work and applications in an easily understood manner. Chapters show that new directions in probability have been suggested by the application of probability to other fields and other disciplines of mathematics. The study of polymer chains in chemistry led to the study of self-avoiding random walks; the study of the Ising model in physics and models for epidemics in biology led to the study of the probability theory of interacting particle systems. The stochastic calculus has allowed probabilists to solve problems in classical analysis, in theory of investment, and in engineering. The mathematical formulation of game theory has led to new insights into decisions under uncertainty. These new developments in probability are vividly illustrated throughout the book.

Stochastic processes --- Probabilities --- Probabilités --- Processus stochastiques --- Probabilities. --- Stochastic processes. --- Probabilités

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Markov random fields --- Markov random fields. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- 519.217 --- Markov processes --- 519.217 Markov processes --- Fields, Markov random --- Random fields

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microbiologie --- biologie --- General microbiology --- Culture Media. --- Microbiological Techniques. --- Microbiologic Technic --- Microbiologic Technics --- Microbiologic Technique --- Microbiological Technics --- Technic, Microbiologic --- Technics, Microbiological --- Technique, Microbiologic --- Techniques, Microbiologic --- Microbiologic Techniques --- Microbiological Technic --- Microbiological Technique --- Technic, Microbiological --- Technics, Microbiologic --- Technique, Microbiological --- Techniques, Microbiological --- Microbiology --- Media, Culture --- Bacteriological Techniques --- methods --- Cultures and culture media --- Handbooks, manuals, etc. --- Culture Media --- Microbiological Techniques --- Microbial biology --- Biology --- Microorganisms --- Cultures and culture media&delete& --- Handbooks, manuals, etc --- Fungi. --- Bacteria --- Yeasts

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Markov processes --- Markov, Processus de --- 519.21 --- 519.217 --- AA / International- internationaal --- 303.0 --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Probability theory. Stochastic processes --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken). --- Markov processes. --- 519.217 Markov processes --- 519.21 Probability theory. Stochastic processes --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken)

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This textbook provides a systematic treatment of denumerable Markov chains, covering both the foundations of the subject and some in topics in potential theory and boundary theory. It is a discussion of relations among what might be called the descriptive quantities associated with Markov chains-probabilities of events and means of random variables that give insight into the behavior of the chains. The approach, by means of infinite matrices, simplifies the notation, shortens statements and proofs of theorems, and often suggests new results. This second edition includes the new chapter, Introduction to Random Fields, written by David Griffeath.

Markov processes. --- Markov processes --- 519.217 --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- 519.217 Markov processes --- Mathematical statistics --- Markov, Processus de