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Lévy Processes in Lie Groupsby Ming Liao; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak; B. Simon
Cambridge University Press 2004; US$ 82.00The theory of Lévy processes in Lie groups is not merely an extension of the theory of Lévy processes in Euclidean spaces. Because of the unique structures possessed by non-commutative Lie groups, these processes exhibit certain interesting limiting properties which are not present in the Euclidean case. A necessary purchase for all whose research brings them into contact with Lévy processes. more...
Elements of the Random Walkby Joseph Rudnick; George Gaspari
Cambridge University Press 2004; US$ 42.00Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. This self-contained text will appeal to graduate students who need to understand the applications of random walk techniques, as well as to established researchers. more...
Lévy Processes and Stochastic Calculusby David Applebaum; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak; B. Simon; B. Totaro
Cambridge University Press 2004; US$ 87.00For the first time in a book, Applebaum ties Lévy processes and stochastic calculus together. All the tools needed for the stochastic approach to option pricing, including Itô's formula, Girsanov's theorem and the martingale representation theorem are described. more...
Dynamic Random Walksby Nadine Guillotin-Plantard; Rene Schott
Elsevier 2006; US$ 109.00The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer science, mathematical physics and finance. Each chapter contains didactical material as well as more advanced technical sections. Few appendices will help refreshing memories (if necessary!). ˇ New probabilistic model, new results in probability theory ˇ Original applications in computer science ˇ Applications in mathematical physics ˇ Applications in finance more...
Random Walk In Random And Non-random Environments (second Edition)by Pál Révész
World Scientific 2005; US$ 135.00The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results ? mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk. Since the first edition was published in 1990, a number of new results have appeared in the literature. The original edition contained many unsolved... more...
Random Walks and Geometryby Vadim A. Kaimanovich
Walter de Gruyter, Inc. 2004; US$ 168.95Recent developments show that probability methods have become a very powerful tool in such different areas as statistical physics, dynamical systems, Riemannian geometry, group theory, harmonic analysis, graph theory and computer science. This volume is an outcome of the special semester 2001 - Random Walks held at the Schrodinger Institute in Vienna, Austria. It contains original research articles with non-trivial new approaches based on applications of random walks and similar processes to Lie groups, geometric flows, physical models on infinite graphs, random number generators, Lyapunov exponents, geometric group theory, spectral theory of graphs and potential theory. more...
Stopped Random Walksby Allan Gut
Springer 2009; US$ 49.95Classical probability theory provides information about random walks after a fixed number of steps. This title shows how this theory can be used to prove limit theorems for renewal counting processes, first passage time processes, and certain two-dimensional random walks, as well as how these results may be used in a variety of applications. more...
Lévy Processes and Stochastic Calculusby David Applebaum
Cambridge University Press 2009; US$ 59.00A fully revised and appended edition of this unique volume, which develops together these two important subjects. more...
Asymptotic Analysis of Random Walksby A. A. Borovkov; K. A. Borovkov
Cambridge University Press 2008; US$ 162.00A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks. more...
Random Walks and Diffusions on Graphs and Databasesby Philippe Blanchard; Dimitri Volchenkov
Springer 2011; US$ 124.00Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks,... more...
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