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Stochastic Dynamics
Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.
Diffusion Processes and Related Problems in Analysis, Volume II
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. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics a...
Spatial Stochastic Processes
This volume has been created in honor of the seventieth birthday of Ted Harris, which was celebrated on January 11th, 1989. The papers rep resent the wide range of subfields of probability theory in which Ted has made profound and fundamental contributions. This breadth in Ted's research complicates the task of putting together in his honor a book with a unified theme. One common thread noted was the spatial, or geometric, aspect of the phenomena Ted investigated. 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. These four topics do not· ex...
Real and Stochastic AnalysisRecent Advances
Real and Stochastic Analysis: Recent Advances presents a carefully edited collection of research articles written by research mathematicians and highlighting advances in RSA. A balanced blend of both theory and applications, this book covers six aspects of stochastic analysis in depth and detail. The first chapters cover the state of the art in tracers analysis, stochastic modeling as it applies to AIDS epidemiology, and the current state of higher order SDEs. Subsequent chapters present a simple approach to Gaussian dichotomy, an overview of harmonizable processes, and stochastic Fubini and Green theorems. Common to all the chapters, the employment of functional analytic methods creates a unified approach. Each chapter includes detailed proofs. Throughout the book, a substantial amount of new material is presented, much of it for the first time. This forward-looking work presents current accounts of important areas of research, evaluates recent advances, and identifies research frontiers and new challenges.
Stochastic Analysis
This book deals with current developments in stochastic analysis and its interfaces with partial differential equations, dynamical systems, mathematical physics, differential geometry, and infinite-dimensional analysis. The origins of stochastic analysis can be found in Norbert Wiener's construction of Brownian motion and Kiyosi Itô's subsequent development of stochastic integration and the closely related theory of stochastic (ordinary) differential equations. The papers in this volume indicate the great strides that have been made in recent years, exhibiting the tremendous power and diversity of stochastic analysis while giving a clear indication of the unsolved problems and possible future directions for development. The collection represents the proceedings of the AMS Summer Institute on Stochastic Analysis, held in July 1993 at Cornell University. Many of the papers are largely expository in character while containing new results.
Dirichlet Forms and Related Topics
This conference proceeding contains 27 peer-reviewed invited papers from leading experts as well as young researchers all over the world in the related fields that Professor Fukushima has made important contributions to. These 27 papers cover a wide range of topics in probability theory, ranging from Dirichlet form theory, Markov processes, heat kernel estimates, entropy on Wiener spaces, analysis on fractal spaces, random spanning tree and Poissonian loop ensemble, random Riemannian geometry, SLE, space-time partial differential equations of higher order, infinite particle systems, Dyson model, functional inequalities, branching process, to machine learning and Hermitizable problems for complex matrices. Researchers and graduate students interested in these areas will find this book appealing.
Stochastic Partial Differential Equations: Six Perspectives
Presents the main topics of interest in the field of stochastic partial differential equations (SPDEs), emphasizing breakthroughs and such basic issues as the role of SPDEs in stochastic modeling, how SPDEs arise, and how their theory is applied in different disciplines. Emphasis is placed on the genesis and applications of SPDEs, as well as mathematical theory and numerical methods. Suitable for graduate level students, researchers. Annotation copyrighted by Book News, Inc., Portland, OR
Séminaire de Probabilités XLIV
As usual, some of the contributions to this 44th Séminaire de Probabilités were presented during the Journées de Probabilités held in Dijon in June 2010. The remainder were spontaneous submissions or were solicited by the editors. The traditional and historical themes of the Séminaire are covered, such as stochastic calculus, local times and excursions, and martingales. Some subjects already touched on in the previous volumes are still here: free probability, rough paths, limit theorems for general processes (here fractional Brownian motion and polymers), and large deviations. Lastly, this volume explores new topics, including variable length Markov chains and peacocks. We hope that the whole volume is a good sample of the main streams of current research on probability and stochastic processes, in particular those active in France.
