Large Deviations Free Energy Functional And Quasi Potential For A Mean Field Model Of Interacting Diffusions
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Large Deviations Free Energy Functional And Quasi Potential For A Mean Field Model Of Interacting Diffusions
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Author : Donald Andrew Dawson
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Large Deviations Free Energy Functional And Quasi Potential For A Mean Field Model Of Interacting Diffusions written by Donald Andrew Dawson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Large deviations for an exchangeable system of reversible diffusions in [double-struck]R[superscript italic]d are investigated in the limit when the number of particles tends to infinity with the objective of providing a methodology to study dynamical phase transitions, tunnelling and metastability for the class of mean field models in statistical physics.
Large Deviations For Stochastic Processes
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Author : Jin Feng
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-03
Large Deviations For Stochastic Processes written by Jin Feng and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-03 with Mathematics categories.
The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.
Probability In Complex Physical Systems
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Author : Jean-Dominique Deuschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23
Probability In Complex Physical Systems written by Jean-Dominique Deuschel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-23 with Mathematics categories.
Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues – one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world’s leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and Jürgen Gärtner, whose scientific work has profoundly influenced the field and all of the present contributions.
Stochastic Partial Differential Equations
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Author : Alison Etheridge
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-13
Stochastic Partial Differential Equations written by Alison Etheridge and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-13 with Mathematics categories.
Consists of papers given at the ICMS meeting held in 1994 on this topic, and brings together some of the world's best known authorities on stochastic partial differential equations.
Handbook On Systemic Risk
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Author : Jean-Pierre Fouque
language : en
Publisher: Cambridge University Press
Release Date : 2013-05-23
Handbook On Systemic Risk written by Jean-Pierre Fouque and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-23 with Business & Economics categories.
The Handbook on Systemic Risk, written by experts in the field, provides researchers with an introduction to the multifaceted aspects of systemic risks facing the global financial markets. The Handbook explores the multidisciplinary approaches to analyzing this risk, the data requirements for further research, and the recommendations being made to avert financial crisis. The Handbook is designed to encourage new researchers to investigate a topic with immense societal implications as well as to provide, for those already actively involved within their own academic discipline, an introduction to the research being undertaken in other disciplines. Each chapter in the Handbook will provide researchers with a superior introduction to the field and with references to more advanced research articles. It is the hope of the editors that this Handbook will stimulate greater interdisciplinary academic research on the critically important topic of systemic risk in the global financial markets.
Large Scale Dynamics Of Interacting Particles
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Author : Herbert Spohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Large Scale Dynamics Of Interacting Particles written by Herbert Spohn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the explanation of large-scale dynamics (evolution differential equations) from models of a very large number of interacting particles. This book addresses both researchers and students. Much of the material presented has never been published in book-form before.
Schr Dinger Equations And Diffusion Theory
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Author : Masao Nagasawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-13
Schr Dinger Equations And Diffusion Theory written by Masao Nagasawa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-13 with Mathematics categories.
Schrödinger Equations and Diffusion Theory addresses the question “What is the Schrödinger equation?” in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger’s conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level. --- This book is a self-contained, very well-organized monograph recommended to researchers and graduate students in the field of probability theory, functional analysis and quantum dynamics. (...) what is written in this book may be regarded as an introduction to the theory of diffusion processes and applications written with the physicists in mind. Interesting topics present themselves as the chapters proceed. (...) this book is an excellent addition to the literature of mathematical sciences with a flavour different from an ordinary textbook in probability theory because of the author’s great contributions in this direction. Readers will certainly enjoy the topics and appreciate the profound mathematical properties of diffusion processes. (Mathematical Reviews)
Seminar On Stochastic Analysis Random Fields And Applications
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Author : Erwin Bolthausen
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Seminar On Stochastic Analysis Random Fields And Applications written by Erwin Bolthausen and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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; taken together, they will apprise the reader of much of the current activity in the area.
Schr Dinger Diffusion Processes
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Author : Robert Aebi
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Schr Dinger Diffusion Processes written by Robert Aebi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In 1931 Erwin Schrödinger considered the following problem: A huge cloud of independent and identical particles with known dynamics is supposed to be observed at finite initial and final times. What is the "most probable" state of the cloud at intermediate times? The present book provides a general yet comprehensive discourse on Schrödinger's question. Key roles in this investigation are played by conditional diffusion processes, pairs of non-linear integral equations and interacting particles systems. The introductory first chapter gives some historical background, presents the main ideas in a rather simple discrete setting and reveals the meaning of intermediate prediction to quantum mechanics. In order to answer Schrödinger's question, the book takes three distinct approaches, dealt with in separate chapters: transformation by means of a multiplicative functional, projection by means of relative entropy, and variation of a functional associated to pairs of non-linear integral equations. The book presumes a graduate level of knowledge in mathematics or physics and represents a relevant and demanding application of today's advanced probability theory.
Stochastic Models
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Author : Donald Andrew Dawson
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Stochastic Models written by Donald Andrew Dawson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book presents the refereed proceedings of the International Conference on Stochastic Models held in Ottawa (ON, Canada) in honor of Professor Donald A. Dawson. Contributions to the volume were written by students and colleagues of Professor Dawson, many of whom are eminent researchers in their own right. A main theme of the book is the development and study of the Dawson-Watanabe "superprocess", a fundamental building block in modelling interaction particle systems undergoing reproduction and movement. The volume also contains an excellent review article by Professor Dawson and a complete list of his work. This comprehensive work offers a wide assortment of articles on Markov processes, branching processes, mathematical finance, filtering, queueing networks, time series, and statistics. It should be of interest to a broad mathematical audience.