Evolution Processes And The Feynman Kac Formula
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Evolution Processes And The Feynman Kac Formula
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Author : Brian Jefferies
language : en
Publisher:
Release Date : 2014-01-15
Evolution Processes And The Feynman Kac Formula written by Brian Jefferies and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Evolution Processes And The Feynman Kac Formula
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Author : Brian Jefferies
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Evolution Processes And The Feynman Kac Formula written by Brian Jefferies 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 2013-03-09 with Mathematics categories.
This book is an outgrowth of ideas originating from 1. Kluvanek. Unfortunately, Professor Kluvanek did not live to contribute to the project of writing up in a systematic form, the circle of ideas to which the present work is devoted. It is more than likely that with his input, the approach and areas of emphasis of the resulting exposition would have been quite different from what we have here. Nevertheless, the stamp of Kluvanek's thought and philosophy (but not necessarily his approval) abounds throughout this book. Although the title gives no indication, integration theory in vector spaces is a cen tral topic of this work. However, the various notions of integration developed here are intimately connected with a specific application-the representation of evolutions by func tional integrals. The representation of a perturbation to the heat semigroup in terms of Wiener measure is known as the Feynman-Kac formula, but the term has a wider meaning in the present work. Traditionally, such representations have been used to obtain analytic information about perturbations to free evolutions as an alternative to arguments with a more operator-theoretic flavour. No applications of this type are given here. It is an un derlying assumption of the presentation of this material that representations of the nature of the Feynman-Kac formula are worth obtaining, and in the process of obtaining them, we may be led to new, possibly fertile mathematical structures-a view largely motivated by the pervasive use of path integrals in quantum physics.
Markov Processes Feller Semigroups And Evolution Equations
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Author : J. A. van Casteren
language : en
Publisher: World Scientific
Release Date : 2011
Markov Processes Feller Semigroups And Evolution Equations written by J. A. van Casteren and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.
Feynman Kac Formulae
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Author : Pierre Del Moral
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-03-30
Feynman Kac Formulae written by Pierre Del Moral 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 2004-03-30 with Mathematics categories.
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.
Theoretical Aspects Of Evolutionary Computing
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Author : Leila Kallel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Theoretical Aspects Of Evolutionary Computing written by Leila Kallel 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 2013-03-09 with Computers categories.
During the first week of September 1999, the Second EvoNet Summer School on Theoretical Aspects of Evolutionary Computing was held at the Middelheim cam pus of the University of Antwerp, Belgium. Originally intended as a small get together of PhD students interested in the theory of evolutionary computing, the summer school grew to become a successful combination of a four-day workshop with over twenty researchers in the field and a two-day lecture series open to a wider audience. This book is based on the lectures and workshop contributions of this summer school. Its first part consists of tutorial papers which introduce the reader to a num ber of important directions in the theory of evolutionary computing. The tutorials are at graduate level andassume only a basic backgroundin mathematics and com puter science. No prior knowledge ofevolutionary computing or its theory is nec essary. The second part of the book consists of technical papers, selected from the workshop contributions. A number of them build on the material of the tutorials, exploring the theory to research level. Other technical papers may require a visit to the library.
Path Integrals For Stochastic Processes
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Author : Horacio S. Wio
language : en
Publisher: World Scientific
Release Date : 2013
Path Integrals For Stochastic Processes written by Horacio S. Wio and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920''s, corresponding to a sum over random trajectories, anticipating by two decades Feynman''s famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950''s. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations.
Discrete Time Semi Markov Random Evolutions And Their Applications
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Author : Nikolaos Limnios
language : en
Publisher: Springer Nature
Release Date : 2023-07-24
Discrete Time Semi Markov Random Evolutions And Their Applications written by Nikolaos Limnios and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-24 with Mathematics categories.
This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.
Random Evolutions And Their Applications
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Author : Anatoly Swishchuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Random Evolutions And Their Applications written by Anatoly Swishchuk 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.
The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications. In physical language, a random evolution ( RE ) is a model for a dynamical sys tem whose state of evolution is subject to random variations. Such systems arise in all branches of science. For example, random Hamiltonian and Schrodinger equations with random potential in quantum mechanics, Maxwell's equation with a random refractive index in electrodynamics, transport equations associated with the trajec tory of a particle whose speed and direction change at random, etc. There are the examples of a single abstract situation in which an evolving system changes its "mode of evolution" or "law of motion" because of random changes of the "environment" or in a "medium". So, in mathematical language, a RE is a solution of stochastic operator integral equations in a Banach space. The operator coefficients of such equations depend on random parameters. Of course, in such generality , our equation includes any homogeneous linear evolving system. Particular examples of such equations were studied in physical applications many years ago. A general mathematical theory of such equations has been developed since 1969, the Theory of Random Evolutions.
Applied Probability And Stochastic Processes
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Author : V. C. Joshua
language : en
Publisher: Springer Nature
Release Date : 2020-08-29
Applied Probability And Stochastic Processes written by V. C. Joshua and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-29 with Mathematics categories.
This book gathers selected papers presented at the International Conference on Advances in Applied Probability and Stochastic Processes, held at CMS College, Kerala, India, on 7–10 January 2019. It showcases high-quality research conducted in the field of applied probability and stochastic processes by focusing on techniques for the modelling and analysis of systems evolving with time. Further, it discusses the applications of stochastic modelling in queuing theory, reliability, inventory, financial mathematics, operations research, and more. This book is intended for a broad audience, ranging from researchers interested in applied probability, stochastic modelling with reference to queuing theory, inventory, and reliability, to those working in industries such as communication and computer networks, distributed information systems, next-generation communication systems, intelligent transportation networks, and financial markets.
Stochastic Calculus And Brownian Motion
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Author : Tejas Thakur
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Stochastic Calculus And Brownian Motion written by Tejas Thakur and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Stochastic Calculus and Brownian Motion" is a comprehensive guide crafted for students and professionals in mathematical sciences, focusing on stochastic processes and their real-world applications in finance, physics, and engineering. We explore key concepts and mathematical foundations of random movements and their practical implications. At its core, the book delves into Brownian motion, the random movement of particles suspended in a fluid, as described by Robert Brown in the 19th century. This phenomenon forms a cornerstone of modern probability theory and serves as a model for randomness in physical systems and financial models describing stock market behaviors. We also cover martingales, mathematical sequences where future values depend on present values, akin to a fair game in gambling. The book demonstrates how martingales are used to model stochastic processes and their calibration in real-world scenarios. Stochastic calculus extends these ideas into continuous time, integrating calculus with random processes. Our guide provides the tools to understand and apply Itô calculus, crucial for advanced financial models like pricing derivatives and managing risks. Written clearly and systematically, the book includes examples and exercises to reinforce concepts and showcase their real-world applications. It serves as an invaluable resource for students, educators, and professionals globally.