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Schr Dinger Diffusion Processes

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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.

Schr Dinger Diffusion Processes

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Author : Robert Aebi
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-02-29

Schr Dinger Diffusion Processes written by Robert Aebi 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 1996-02-29 with Gardening categories.

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)

Stochastic Processes In Quantum Physics

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Author : Masao Nagasawa
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Stochastic Processes In Quantum Physics written by Masao Nagasawa 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.

"Stochastic Processes in Quantum Physics" addresses the question 'What is the mathematics needed for describing the movement of quantum particles', and shows that it is the theory of stochastic (in particular Markov) processes and that a relativistic quantum particle has pure-jump sample paths while sample paths of a non-relativistic quantum particle are continuous. Together with known techniques, some new stochastic methods are applied in solving the equation of motion and the equation of dynamics of relativistic quantum particles. The problem of the origin of universes is discussed as an application of the theory. The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level, and some selected chapters can be used as (sub-)textbooks for advanced courses on stochastic processes, quantum theory and theoretical chemistry.

Handbooks In Operations Research And Management Science Financial Engineering

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Author : John R. Birge
language : en
Publisher: Elsevier
Release Date : 2007-11-16

Handbooks In Operations Research And Management Science Financial Engineering written by John R. Birge and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-16 with Business & Economics categories.

The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.

Stochastic Processes Physics And Geometry Ii Proceedings Of The Iii International Conference

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Author : Sergio Albeverio
language : en
Publisher: World Scientific
Release Date : 1995-02-17

Stochastic Processes Physics And Geometry Ii Proceedings Of The Iii International Conference written by Sergio Albeverio and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-17 with categories.

As was already evident from the previous two meetings, the theory of stochastic processes, the study of geometrical structures, and the investigation of certain physical problems are inter-related. In fact the trend in recent years has been towards stronger interactions between these areas. As a result, a large component of the contributions is concerned with the theory of stochastic processes, quantum theory, and their relations.

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.

It S Stochastic Calculus And Probability Theory

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Author : Nobuyuki Ikeda
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

It S Stochastic Calculus And Probability Theory written by Nobuyuki Ikeda 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 Mathematics categories.

Professor Kiyosi Ito is well known as the creator of the modern theory of stochastic analysis. Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater. For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future. For example, a basic formula, called the Ito formula, is well known and widely used in fields as diverse as physics and economics. This volume contains 27 papers written by world-renowned probability theorists. Their subjects vary widely and they present new results and ideas in the fields where stochastic analysis plays an important role. Also included are several expository articles by well-known experts surveying recent developments. Not only mathematicians but also physicists, biologists, economists and researchers in other fields who are interested in the effectiveness of stochastic theory will find valuable suggestions for their research. In addition, students who are beginning their study and research in stochastic analysis and related fields will find instructive and useful guidance here. This volume is dedicated to Professor Ito on the occasion of his eightieth birthday as a token of deep appreciation for his great achievements and contributions. An introduction to and commentary on the scientific works of Professor Ito are also included.

Schrodinger

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Author : Walter Moore
language : en
Publisher: Cambridge University Press
Release Date : 2015-10-06

Schrodinger written by Walter Moore 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 2015-10-06 with Biography & Autobiography categories.

This is a biography of the great scientist, Erwin Schrödinger (author of What is Life?), which draws upon recollections of his family and friends, as well as on contemporary records, diaries and letters. It aims to reveal the fundamental motives that drove him.

Handbook Of Brownian Motion

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Author : Andrei Borodin
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Handbook Of Brownian Motion written by Andrei Borodin 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.

There are two parts in this book. The first part is devoted mainly to the proper ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distributions of functionals of Brownian motion and re lated processes. The primary aim of this book is to give an easy reference to a large number of facts and formulae associated to Brownian motion. We have tried to do this in a "handbook-style". By this we mean that results are given without proofs but are equipped with a reference where a proof or a derivation can be found. It is our belief and experience that such a material would be very much welcome by students and people working with applications of diffusions and Brownian motion. In discussions with many of our colleagues we have found that they share this point of view. Our original plan included more things than we were able to realize. It turned out very soon when trying to put the plan into practice that the material would be too wide to be published under one cover. Excursion theory, which most of the recent results concerning linear Brownian motion and diffusions can be classified as, is only touched upon slightly here, not to mention Brownian motion in several dimensions which enters only through the discussion of Bessel processes. On the other hand, much attention is given to the theory of local time.

Schr Dinger Diffusion Processes

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