Non Autonomous Kato Classes And Feynman Kac Propagators

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Non Autonomous Kato Classes And Feynman Kac Propagators

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Author : Archil Gulisashvili
language : en
Publisher: World Scientific
Release Date : 2006

Non Autonomous Kato Classes And Feynman Kac Propagators written by Archil Gulisashvili and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

"This book provides an introduction to propagator theory. Propagators, or evolution families, are two-parameter analogues of semigroups of operators. Propagators are encountered in analysis, mathematical physics, partial differential equations, and probability theory. They are often used as mathematical models of systems evolving in a changing environment. A unifying theme of the book is the theory of Feynman-Kac propagators associated with time-dependent measures from non-autonomous Kato classes. In applications, a Feynman-Kac propagator describes the evolution of a physical system in the presence of time-dependent absorption and excitation. The book is suitable as an advanced textbook for graduate courses." "Readership: Graduate students and researchers in mathematical analysis, partial differential equations, and probability theory."--BOOK JACKET.

Non Autonomous Kato Classes And Feynman Kac Propagators

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Author : Archil Gulisashvili
language : en
Publisher: World Scientific
Release Date : 2006-07-14

Non Autonomous Kato Classes And Feynman Kac Propagators written by Archil Gulisashvili and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-14 with Mathematics categories.

This book provides an introduction to propagator theory. Propagators, or evolution families, are two-parameter analogues of semigroups of operators. Propagators are encountered in analysis, mathematical physics, partial differential equations, and probability theory. They are often used as mathematical models of systems evolving in a changing environment. A unifying theme of the book is the theory of Feynman-Kac propagators associated with time-dependent measures from non-autonomous Kato classes. In applications, a Feynman-Kac propagator describes the evolution of a physical system in the presence of time-dependent absorption and excitation. The book is suitable as an advanced textbook for graduate courses.

Seminar Of Mathematical Analysis

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Author : Genaro López Acedo
language : en
Publisher: Universidad de Sevilla
Release Date : 2004

Seminar Of Mathematical Analysis written by Genaro López Acedo and has been published by Universidad de Sevilla this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematical analysis categories.

This volume consists of the lecture notes of the Seminar on Mathematical Analysis which was held at the Universities of Malaga and Seville, Septembre 2002-February 2003.

Functional Analysis And The Feynman Operator Calculus

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Author : Tepper Gill
language : en
Publisher: Springer
Release Date : 2016-03-30

Functional Analysis And The Feynman Operator Calculus written by Tepper Gill and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-30 with Mathematics categories.

This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.

Kolmogorov Operators And Their Applications

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Author : Stéphane Menozzi
language : en
Publisher: Springer Nature
Release Date : 2024-05-29

Kolmogorov Operators And Their Applications written by Stéphane Menozzi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-29 with Mathematics categories.

Kolmogorov equations are a fundamental bridge between the theory of partial differential equations and that of stochastic differential equations that arise in several research fields. This volume collects a selection of the talks given at the Cortona meeting by experts in both fields, who presented the most recent developments of the theory. Particular emphasis has been given to degenerate partial differential equations, Itô processes, applications to kinetic theory and to finance.

Functional Analysis And Evolution Equations

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Author : Herbert Amann
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-28

Functional Analysis And Evolution Equations written by Herbert Amann 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 2008-02-28 with Mathematics categories.

Gunter Lumer was an outstanding mathematician whose works have great influence on the research community in mathematical analysis and evolution equations. He was at the origin of the breath-taking development the theory of semigroups saw after the pioneering book of Hille and Phillips from 1957. This volume contains invited contributions presenting the state of the art of these topics and reflecting the broad interests of Gunter Lumer.

Inhomogeneous Random Evolutions And Their Applications

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Author : Anatoliy Swishchuk
language : en
Publisher: CRC Press
Release Date : 2019-12-11

Inhomogeneous Random Evolutions And Their Applications written by Anatoliy Swishchuk and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-11 with Mathematics categories.

Inhomogeneous Random Evolutions and Their Applications explains how to model various dynamical systems in finance and insurance with non-homogeneous in time characteristics. It includes modeling for: financial underlying and derivatives via Levy processes with time-dependent characteristics; limit order books in the algorithmic and HFT with counting price changes processes having time-dependent intensities; risk processes which count number of claims with time-dependent conditional intensities; multi-asset price impact from distressed selling; regime-switching Levy-driven diffusion-based price dynamics. Initial models for those systems are very complicated, which is why the author’s approach helps to simplified their study. The book uses a very general approach for modeling of those systems via abstract inhomogeneous random evolutions in Banach spaces. To simplify their investigation, it applies the first averaging principle (long-run stability property or law of large numbers [LLN]) to get deterministic function on the long run. To eliminate the rate of convergence in the LLN, it uses secondly the functional central limit theorem (FCLT) such that the associated cumulative process, centered around that deterministic function and suitably scaled in time, may be approximated by an orthogonal martingale measure, in general; and by standard Brownian motion, in particular, if the scale parameter increases. Thus, this approach allows the author to easily link, for example, microscopic activities with macroscopic ones in HFT, connecting the parameters driving the HFT with the daily volatilities. This method also helps to easily calculate ruin and ultimate ruin probabilities for the risk process. All results in the book are new and original, and can be easily implemented in practice.

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.

Analytically Tractable Stochastic Stock Price Models

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Author : Archil Gulisashvili
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-04

Analytically Tractable Stochastic Stock Price Models written by Archil Gulisashvili 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 2012-09-04 with Mathematics categories.

Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility. One of the author's main goals is to provide sharp asymptotic formulas with error estimates for distribution densities of stock prices, option pricing functions, and implied volatilities in various stochastic volatility models. The author also establishes sharp asymptotic formulas for the implied volatility at extreme strikes in general stochastic stock price models. The present volume is addressed to researchers and graduate students working in the area of financial mathematics, analysis, or probability theory. The reader is expected to be familiar with elements of classical analysis, stochastic analysis and probability theory.

Stochastic Analysis A Series Of Lectures

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Author : Robert C. Dalang
language : en
Publisher: Birkhäuser
Release Date : 2015-07-28

Stochastic Analysis A Series Of Lectures written by Robert C. Dalang and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-28 with Mathematics categories.

This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields of stochastic analysis and mathematical physics. Contributors: S. Albeverio M. Arnaudon V. Bally V. Barbu H. Bessaih Z. Brzeźniak K. Burdzy A.B. Cruzeiro F. Flandoli A. Kohatsu-Higa S. Mazzucchi C. Mueller J. van Neerven M. Ondreját S. Peszat M. Veraar L. Weis J.-C. Zambrini