Download or read book Diffusion Processes and Related Problems in Analysis Volume II written by V. Wihstutz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.
Download or read book Diffusion Processes and Related Problems in Analysis written by Mark A. Pinsky and published by . This book was released on 2011-09-26 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Diffusion Processes and Related Problems in Analysis written by Mark A. Pinsky and published by Springer Science & Business Media. This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Diffusion Processes and Related Problems in Analysis Volume I written by and published by . This book was released on 1990 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Diffusion Processes and Related Topics in Biology written by Luigi M. Ricciardi and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a one-quarter course given at the Department of Biophysics and Theoretical Biology of the University of Chicago in 1916. The course was directed to graduate students in the Division of Biological Sciences with interests in population biology and neurobiology. Only a slight acquaintance with probability and differential equations is required of the reader. Exercises are interwoven with the text to encourage the reader to play a more active role and thus facilitate his digestion of the material. One aim of these notes is to provide a heuristic approach, using as little mathematics as possible, to certain aspects of the theory of stochastic processes that are being increasingly employed in some of the population biol ogy and neurobiology literature. While the subject may be classical, the nov elty here lies in the approach and point of view, particularly in the applica tions such as the approach to the neuronal firing problem and its related dif fusion approximations. It is a pleasure to thank Professors Richard C. Lewontin and Arnold J.F. Siegert for their interest and support, and Mrs. Angell Pasley for her excellent and careful typing. I . PRELIMINARIES 1. Terminology and Examples Consider an experiment specified by: a) the experiment's outcomes, ~, forming the space S; b) certain subsets of S (called events) and by the probabilities of these events.
Download or read book Diffusion Processes and Related Problems in Analysis Volume I written by Pinsky and published by Birkhäuser. This book was released on 2013-05-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the week of October 23-27,1989, Northwestern University hosted an international conference on the theme "Diffusion Processes and Related Problems in Analysis." This was attended by 105 partici pants representing 14 different countries. 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. The purpose of this meeting was to bring together workers in vari ous parts of probability theory, mathematical physics, and partial dif ferential equations. Previous efforts in this direction were represented by the 1987 AMS Summer Research Conference "Geometry of Random Motion" co-sponsored with Rick Durrett, the proceedings of which ap peared as volume 73 in the AMS series "Contemporary Mathematics." The present effort is intended to extend beyond the strictly geometric theme and to include problems of large deviations, stochastic flows, and other areas of stochastic analysis in which diffusion processes play a leading role.
Download or read book Diffusion Processes and Related Problems in Analysis Volume I written by Pinsky and published by Birkhäuser. This book was released on 2012-02-17 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the week of October 23-27,1989, Northwestern University hosted an international conference on the theme "Diffusion Processes and Related Problems in Analysis." This was attended by 105 partici pants representing 14 different countries. 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. The purpose of this meeting was to bring together workers in vari ous parts of probability theory, mathematical physics, and partial dif ferential equations. Previous efforts in this direction were represented by the 1987 AMS Summer Research Conference "Geometry of Random Motion" co-sponsored with Rick Durrett, the proceedings of which ap peared as volume 73 in the AMS series "Contemporary Mathematics." The present effort is intended to extend beyond the strictly geometric theme and to include problems of large deviations, stochastic flows, and other areas of stochastic analysis in which diffusion processes play a leading role.
Download or read book Random Perturbation Methods with Applications in Science and Engineering written by Anatoli V. Skorokhod and published by Springer Science & Business Media. This book was released on 2007-06-21 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.
Download or read book Stochastic Analysis and Related Topics VII written by Laurent Decreusefond and published by Springer Science & Business Media. This book was released on 2001-01-25 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.
Download or read book Stochastic Analysis and Related Topics written by H. Körezlioglu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a large spectrum of work: super processes, Dirichlet forms, anticipative stochastic calculus, random fields and Wiener space analysis. The first part of the volume consists of two main lectures given at the third Silivri meeting in 1990: 1. "Infinitely divisible random measures and superprocesses" by D.A. Dawson, 2. "Dirichlet forms on infinite dimensional spaces and appli cations" by M. Rockner. The second part consists of recent research papers all related to Stochastic Analysis, motivated by stochastic partial differ ential equations, Markov fields, the Malliavin calculus and the Feynman path integrals. We would herewith like to thank the ENST for its material support for the above mentioned meeting as well as for the ini tial preparation of this volume and to our friend and colleague Erhan Qmlar whose help and encouragement for the realization of this volume have been essential. H. Korezlioglu A.S. Ustiinel INFINITELY DIVISIBLE RANDOM MEASURES AND SUPERPROCESSES DONALD A. DAWSON 1. Introduction.
Download or read book Stochastic Analysis and Diffusion Processes written by Gopinath Kallianpur and published by OUP Oxford. This book was released on 2014-01-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.
Download or read book New Trends in Stochastic Analysis and Related Topics written by Huaizhong Zhao and published by World Scientific. This book was released on 2012 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.
Download or read book Seminar on Stochastic Processes 1992 written by Cinlar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1992 Seminar on Stochastic Processes was held at the Univer sity of Washington from March 26 to March 28, 1992. This was the twelfth in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, University of Florida, University of Virginia, University of California, San Diego, University of British Columbia and University of California, Los An geles. Following the successful format of previous years, there were five invited lectures, delivered by R. Adler, R. Banuelos, J. Pitman, S. J. Taylor and R. Williams, with the remainder of the time being devoted to informal communications and workshops on current work and problems. The enthusiasm and interest of the participants cre ated a lively and stimulating atmosphere for the seminar. A sample of the research discussed there is contained in this volume. The 1992 Seminar was made possible through the support of the National Science Foundation, the National Security Agency, the Institute of Mathematical Statistics and the University of Washing ton. We extend our thanks to them and to the publisher Birkhauser Boston for their support and encouragement. Richard F. Bass Krzysztof Burdzy Seattle, 1992 SUPERPROCESS LOCAL AND INTERSECTION LOCAL TIMES AND THEIR CORRESPONDING PARTICLE PICTURES Robert J.
Download or read book Stochastic Partial Differential Equations and Related Fields written by Andreas Eberle and published by Springer. This book was released on 2018-07-03 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.
Download or read book Random Dynamical Systems written by Ludwig Arnold and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
Download or read book The Dynkin Festschrift written by Mark I. Freidlin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Onishchik, A. A. Kirillov, and E. B. Vinberg, who obtained their first results on Lie groups in Dynkin's seminar. At a later stage, the work of the seminar was greatly enriched by the active participation of 1. 1. Pyatetskii Shapiro. As already noted, Dynkin started to work in probability as far back as his undergraduate studies. In fact, his first published paper deals with a problem arising in Markov chain theory. The most significant among his earliest probabilistic results concern sufficient statistics. In [15] and [17], Dynkin described all families of one-dimensional probability distributions admitting non-trivial sufficient statistics. These papers have considerably influenced the subsequent research in this field. 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. He created the fundamental concept of a Markov process as a family of measures corresponding to var ious initial times and states and he defined time homogeneous processes in terms of the shift operators ()t. In a joint paper with his student A.
Download or read book Analysis for Diffusion Processes on Riemannian Manifolds written by Feng-Yu Wang and published by World Scientific. This book was released on 2014 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.
