Bücher der Reihe Progress in Probability

The conference, which is part of the "Emphasis Year" program traditionally supported by the Mathematics Department, was additionally supported by grants from the National Science Foundation, the National Security Agency, the Institute for Mathematics and Applications, as well as by supplemen tary sources from Northwestern University.

Pure and applied stochastic analysis and random fields form the subject of this book. The collection of articles on these topics represent the state of the art of the research in the field, with particular attention being devoted to stochastic models in finance. Some are review articles, others are original papers;

These developments have been triggered to a large part by the mathem- ical understanding gained on the fascinating and previously mysterious "Parisi solution" of the Sherrington-Kirkpatrick mean ?eld model of spin glasses, due to the work of Guerra, Talagrand, and others.

Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times.

These proceedings represent the current state of research on the topics 'boundary theory' and 'spectral and probability theory' of random walks on infinite graphs.

This volume contains refereed research or review papers presented at the 6th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verita) in Ascona, Switzerland, in May 2008.

Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times.

This volume has been created in honor of the seventieth birthday of Ted Harris, which was celebrated on January 11th, 1989. This volume has been organized around that theme, with papers covering four major subject areas of Ted's research: branching processes, percola tion, interacting particle systems, and stochastic flows.

Fractal geometry is used to model complicated natural and technical phenomena in various disciplines like physics, biology, finance, and medicine. Since most convincing models contain an element of randomness, stochastics enters the area in a natural way. This book documents the establishment of fractal geometry as a substantial mathematical theory. As in the previous volumes, which appeared in 1998 and 2000, leading experts known for clear exposition were selected as authors. They survey their field of expertise, emphasizing recent developments and open problems. Main topics include multifractal measures, dynamical systems, stochastic processes and random fractals, harmonic analysis on fractals.

This volume contains 20 refereed research or review papers presented at the five-day Third Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verita) in Ascona, Switzerland, from September 20 to 24, 1999.

Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics.

This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance.

Over the last years, stochastic analysis has had an enormous progress with the impetus originating from different branches of mathematics: PDE's and the Malliavin calculus, quantum physics, path space analysis on curved manifolds via probabilistic methods, and more. This volume contains selected contributions which were presented at the 8th Silivri Workshop on Stochastic Analysis and Related Topics, held in September 2000 in Gazimagusa, North Cyprus. The topics include stochastic control theory, generalized functions in a nonlinear setting, tangent spaces of manifold-valued paths with quasi-invariant measures, and applications in game theory, theoretical biology and theoretical physics. Contributors: A.E. Bashirov, A. Bensoussan and J. Frehse, U. Capar and H. Aktuglul, A.B. Cruzeiro and Kai-Nan Xiang, E. Hausenblas, Y. Ishikawa, N. Mahmudov, P. Malliavin and U. Taneri, N. Privault, A.S. Üstünel

Contains refereed research or review articles presented at the 7th Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verita) in Ascona , Switzerland, in May 2011.

Data collection continued throughout the millenia, and although data bases became larger, more re liable, and better codified, it was not really until surprisingly recently that mankind began to try to understand the physics behind these data, and, shortly afterwards, to attempt to model it.

At the end of the summer 1989, an international conference on stochastic analysis and related topics was held for the first time in Lisbon (Portu gal).

This volume features a collection of contributed articles and lecture notes from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013.

Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process.

A collection of 20 refereed research or review papers presented at a six-day seminar in Switzerland. The contributions focus on stochastic analysis, its applications to the engineering sciences, and stochastic methods in financial models, which was the subject of a minisymposium.

This volume contains the proceedings of the vVorkshop on Trees held in Versailles on 14-16 June 1995. Why: a workshop on trees? Two main reasons motivated this workshop. First, the current plethora of tree representations in branching processes which has be­ come obvious by the Minneapolis IMA Congress Classica] and Modern Branching Processes in 1994. But this would not have been sufficient to organize an "n-th" congress on branching processes. Secondly, regular discussions with researchers in algebra and computing sciences at the University of Versailles and at INRIA (lnstitut National de Recherche en Informatique et Automatique) convinced us it would be fruitful to offer the workers in these different fields the opportunity to exchange their points of view on the subject. The organizers being probabilists, a large part of the meeting (two sessions) was devoted t~ probability theor:y (not only branching processes). Nevertheless, the other three sessions focused on algorithms, on ultrametric and combinatorial aspects of trees and on disordered systems. Most papers in this volume are both of high level and of pedagogical interest. They are intended for a large public, including graduate students looking for an initiation to tree structures. The papers have been grouped into four sections: - disordered systems, - probability and trees, - large deviations, - ultrametric and algebraic aspects of trees. Some of the speakers are, unfortunately, not represented in this volume.

These include random matrix theory, nonparametric statistics, empirical process theory, statistical learning theory, concentration of measure phenomena, strong and weak approximations, distribution function estimation in high dimensions, combinatorial optimization, and random graph theory.

This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come.

During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics.

But Dynkin's most famous results in probability concern the theory of Markov processes. Following Kolmogorov, Feller, Doob and Ito, Dynkin opened a new chapter in the theory of Markov processes.