Author : József Lörinczi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 593 pages
File Size : 44,31 MB
Release : 2020-01-20
Category : Mathematics
ISBN : 3110389932
This is the second updated and extended edition of the successful book on Feynman-Kac theory. It offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. The first volume concentrates on Feynman-Kac-type formulae and Gibbs measures.
Author : József Lörinczi
Publisher :
Page : 550 pages
File Size : 50,35 MB
Release : 2015
Category :
ISBN : 9783110330045
Author : József Lörinczi
Publisher : Walter de Gruyter
Page : 521 pages
File Size : 19,25 MB
Release : 2011-08-29
Category : Mathematics
ISBN : 3110203731
This monograph offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. These ideas are then applied principally to a rigorous treatment of some fundamental models of quantum field theory. In this self-contained presentation of the material both beginners and experts are addressed, while putting emphasis on the interdisciplinary character of the subject.
Author : Pierre Del Moral
Publisher : Springer Science & Business Media
Page : 567 pages
File Size : 19,93 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1468493930
This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviation principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods.
Author : Fumio Hiroshima
Publisher : Walter de Gruyter GmbH & Co KG
Page : 558 pages
File Size : 39,91 MB
Release : 2020-03-09
Category : Mathematics
ISBN : 3110403544
This is the second updated and extended edition of the successful book on Feynman-Kac theory. It offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. In the second volume, these ideas are applied principally to a rigorous treatment of some fundamental models of quantum field theory.
Author : Asao Arai
Publisher : Springer Nature
Page : 123 pages
File Size : 29,70 MB
Release : 2022-10-18
Category : Science
ISBN : 9811956782
This book explains the mathematical structures of supersymmetric quantum field theory (SQFT) from the viewpoints of functional and infinite-dimensional analysis. The main mathematical objects are infinite-dimensional Dirac operators on the abstract Boson–Fermion Fock space. The target audience consists of graduate students and researchers who are interested in mathematical analysis of quantum fields, including supersymmetric ones, and infinite-dimensional analysis. The major topics are the clarification of general mathematical structures that some models in the SQFT have in common, and the mathematically rigorous analysis of them. The importance and the relevance of the subject are that in physics literature, supersymmetric quantum field models are only formally (heuristically) considered and hence may be ill-defined mathematically. From a mathematical point of view, however, they suggest new aspects related to infinite-dimensional geometry and analysis. Therefore, it is important to show the mathematical existence of such models first and then study them in detail. The book shows that the theory of the abstract Boson–Fermion Fock space serves this purpose. The analysis developed in the book also provides a good example of infinite-dimensional analysis from the functional analysis point of view, including a theory of infinite-dimensional Dirac operators and Laplacians.
Author : René L. Schilling
Publisher : Walter de Gruyter GmbH & Co KG
Page : 533 pages
File Size : 25,1 MB
Release : 2021-09-07
Category : Mathematics
ISBN : 311074127X
Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''.
Author : Robert Dalang
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 21,98 MB
Release : 2011-03-16
Category : Mathematics
ISBN : 3034800215
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 Verità) in Ascona, Switzerland, in May 2008. The seminar focused mainly on stochastic partial differential equations, especially large deviations and control problems, on infinite dimensional analysis, particle systems and financial engineering, especially energy markets and climate models. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance.
Author : Wolfhard Janke
Publisher : World Scientific
Page : 629 pages
File Size : 31,1 MB
Release : 2008-11-12
Category : Science
ISBN : 9814469149
This proceedings volume contains selected talks and poster presentations from the 9th International Conference on Path Integrals — New Trends and Perspectives, which took place at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, during the period September 23-28, 2007. Continuing the well-developed tradition of the conference series, the present status of both the different techniques of path integral calculations and their diverse applications to many fields of physics and chemistry is reviewed. This is reflected in the main topics in this volume, which range from more traditional fields such as general quantum physics and quantum or statistical field theory through technical aspects like Monte Carlo simulations to more modern applications in the realm of quantum gravity and astrophysics, condensed matter physics with topical subjects such as Bose-Einstein condensation or quantum wires, biophysics and econophysics. All articles are successfully tied together by the common method of path integration; as a result, special methodological advancements in one topic could be transferred to other topics.
Author : Pierre Del Moral
Publisher : CRC Press
Page : 1026 pages
File Size : 12,13 MB
Release : 2017-02-24
Category : Mathematics
ISBN : 1498701868
Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.
