Random And Vector Measures, Rao M M

Автор: Schilling
Название: Measures, Integrals and Martingales
ISBN: 1316620247 ISBN-13(EAN): 9781316620243
Издательство: Cambridge Academ
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Цена: 7445.00 р.
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Описание: Measure and integration are key topics in many areas of mathematics, including analysis, probability, mathematical physics and finance. This book offers a concise yet elementary introduction in which the theory is quickly and simply developed. Few prerequisites are required, making the text suitable for undergraduate lecture courses or self-study.

Автор: G?ran H?gn?s; Arunava Mukherjea
Название: Probability Measures on Semigroups
ISBN: 1461427320 ISBN-13(EAN): 9781461427322
Издательство: Springer
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Цена: 21661.00 р.
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Описание: This book presents up-to-date material on the theory of weak convergence of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices. Includes exercises.

Автор: Rozikov Utkir A
Название: Gibbs Measures On Cayley Trees
ISBN: 9814513377 ISBN-13(EAN): 9789814513371
Издательство: World Scientific Publishing
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Цена: 20592.00 р.
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Описание: The purpose of this book is to present systematically all known mathematical results on Gibbs measures on Cayley trees (Bethe lattices).The Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Moreover, the Gibbs measure is the unique measure that maximizes the entropy for a given expected energy.The method used for the description of Gibbs measures on Cayley trees is the method of Markov random field theory and recurrent equations of this theory, but the modern theory of Gibbs measures on trees uses new tools such as group theory, information flows on trees, node-weighted random walks, contour methods on trees, and nonlinear analysis. This book discusses all the mentioned methods, which were developed recently.