Probability theory on compact Lie groups deals with the interaction between "chance" and "symmetry," a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks...
Probability theory on compact Lie groups deals with the interaction between "chance" and "symmetry," a beautiful area of mathematics of great inter...
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes.
Limit theorems form the backbone of...
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in t...
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues.
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information r...
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept.
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different area...
This book is intended for readers who are quite familiar with probability and stochastic processes but know little or nothing about ?nance. It is written in the de?nition/theorem/proof style of modern mathematics and attempts to explain as much of the ?nance motivation and terminology as possible. A mathematical monograph on ?nance can be written today only - cause of two revolutions that have taken place on Wall Street in the latter half of the twentieth century. Both these revolutions began at universities, albeit in economics departments and business schools, not in departments of...
This book is intended for readers who are quite familiar with probability and stochastic processes but know little or nothing about ?nance. It is writ...
This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts.
Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the...
This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with bou...
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order...
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-ord...
Ces notes sont consacrees aux inegalites et aux theoremes limites classiques pour les suites de variables aleatoires absolument regulieres ou fortement melangeantes au sens de Rosenblatt. Le but poursuivi est de donner des outils techniques pour l'etude des processus faiblement dependants aux statisticiens ou aux probabilistes travaillant sur ces processus.
Ces notes sont consacrees aux inegalites et aux theoremes limites classiques pour les suites de variables aleatoires absolument regulieres ou forte...
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions.
Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the...
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is s...
