“…Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.…”
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“…To illustrate their argument, the authors turn to classic games--backgammon, bridge, and chess--and relate them to physical, biological, and social applications of probability theory and number theory. Further, they have invented, and present here, more than a dozen playable games derived from scientific models for equilibrium, selection, growth, and even the composition of RNA.…”
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“…Following a look at the basic concepts of probability theory, the authors goe on to examine the elements of microhydrodynamics, Brownian motion, and real liquids in turbulent flow. …”
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“…Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.…”
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“…In 1991-94, he served as the Editor-in-Chief of "Probability Theory and Related Fields.".…”
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“…Providing a broad overview of the current state of the art in probability theory and its applications, and featuring an article coauthored by Mark Yor, this volume contains contributions on branching processes, Lévy processes, random walks and martingales and their connection with, among other topics, rough paths, semi-groups, heat kernel asymptotics and mathematical finance.…”
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“…The authors explain numerous peculiarities of stable distributions and describe the principle concept of probability theory and function analysis. A significant part of the book is devoted to applications of stable distributions. …”
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“…The subject of this book is a new direction in the field of probability theory and mathematical statistics which can be called "stability theory": it deals with evaluating the effects of perturbing initial probabilistic models and embraces quite varied subtopics: limit theorems, queueing models, statistical inference, probability metrics, etc. …”
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“…The contributions treat recent developments in analysis and surrounding areas, concerning topics from the theory of partial differential equations, function spaces, scattering, probability theory, and others, as well as applications to biomathematics, queueing models, fractured porous media and geomechanics.…”
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“… This second revised and extended edition presents the fundamental ideas and results of both, probability theory and statistics, and comprises the material of a one-year course. …”
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“…After making some general remarks, I consider two examples that illustrate the use of Bayesian Probability Theory. The first is a simple one, the physicist's favorite "toy," that provides a forum for a discussion of the key conceptual issue of Bayesian analysis: the assignment of prior probabilities. …”
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“…Interestingly, there are several settings, ranging from machine learning on partial data over frequential probability theory to quantum probability theory and decision making under uncertainty, in which, a priori, the probabilities are only desired to be precise on a specific underlying set system. …”
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“…Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. …”
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“…Drills and boxed summaries emphasize and reinforce important ideas and special techniques.Beginning with a review of the basic concepts and methods in probability theory, moments, and moment generating functions, the author moves to more intricate topics. …”
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“…Interactions between the theory of partial differential equations of elliptic and parabolic types and the theory of stochastic processes are beneficial for both probability theory and analysis. At the beginning, mostly analytic results were used by probabilists. …”
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“…Arising from the probability theory and renormalization group methods, this novel approach has been proved recently to provide efficient investigative tools for the collective features that occur in any finite system. …”
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