Generalized Functionals Of Brownian Motion And Their Applications
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Generalized Functionals Of Brownian Motion And Their Applications
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Author : Nasir Uddin Ahmed
language : en
Publisher: World Scientific
Release Date : 2012
Generalized Functionals Of Brownian Motion And Their Applications written by Nasir Uddin Ahmed and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process ? covering the classical Wiener?Ito class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the Wiener?Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems.Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz?Fischer theorem for separable Hilbert spaces and the space of Wiener?Ito functionals is drawn out, thus providing a clear insight into the subject.
Handbook Of Brownian Motion Facts And Formulae
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Author : Andrei N. Borodin
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Handbook Of Brownian Motion Facts And Formulae written by Andrei N. 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.
Here is easy reference to a wealth of facts and formulae associated with Brownian motion, collecting in one volume more than 2500 numbered formulae. The book serves as a basic reference for researchers, graduate students, and people doing applied work with Brownian motion and diffusions, and can be used as a source of explicit examples when teaching stochastic processes.
Handbook Of Brownian Motion
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Author : A. N. Borodin
language : en
Publisher: Birkhauser
Release Date : 2002-01-01
Handbook Of Brownian Motion written by A. N. Borodin and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Brownian motion processes categories.
Probability Statistics And Their Applications
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Author : Rabindra Nath Bhattacharya
language : en
Publisher: IMS
Release Date : 2003
Probability Statistics And Their Applications written by Rabindra Nath Bhattacharya and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Selected Papers Of Takeyuki Hida
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Author : Takeyuki Hida
language : en
Publisher: World Scientific
Release Date : 2001-01-01
Selected Papers Of Takeyuki Hida written by Takeyuki Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
The topics discussed in this book can be classified into three parts: . (i) Gaussian processes. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often and its developments are discussed. (ii) White noise analysis. This book includes the notes of the series of lectures delivered in 1975 at Carleton University in Ottawa. They describe the very original idea of introducing the notion of generalized Brownian functionals (nowadays called OC generalized white noise functionalsOCO, and sometimes OC Hida distributionOCO. (iii) Variational calculus for random fields. This topic will certainly represent one of the driving research lines for probability theory in the next century, as can be seen from several papers in this volume. Sample Chapter(s). Chapter 1: Analysis of Brownian Functionals (1,502 KB). Contents: General Theory of White Noise Functionals; Gaussian and Other Processes; Infinite Dimensional Harmonic Analysis and Rotation Group; Quantum Theory; Feynman Integrals and Random Fields; Variational Calculus and Random Fields; Application to Biology. Readership: Graduate students and researchers in the fields of probability theory, functional analysis, statistics and theoretical physics."
Aspects Of Brownian Motion
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Author : Roger Mansuy
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-16
Aspects Of Brownian Motion written by Roger Mansuy 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 2008-09-16 with Mathematics categories.
Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about Brownian motion and related processes. This book focuses on special classes of Brownian functionals, including Gaussian subspaces of the Gaussian space of Brownian motion; Brownian quadratic funtionals; Brownian local times; Exponential functionals of Brownian motion with drift; Time spent by Brownian motion below a multiple of its one-sided supremum.
Stochastic Processes
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Author : Andrei N Borodin
language : en
Publisher: Birkhäuser
Release Date : 2017-10-30
Stochastic Processes written by Andrei N Borodin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-30 with Mathematics categories.
This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.
Measure Theory And Its Applications
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Author : J.M. Belley
language : en
Publisher: Springer
Release Date : 2006-12-08
Measure Theory And Its Applications written by J.M. Belley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
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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.
Quantum Information V
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Author : T Hida
language : en
Publisher: World Scientific
Release Date : 2006-01-18
Quantum Information V written by T Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-18 with Mathematics categories.
Contents:Recognition and Teleportation (M Ohya et al.)Quantum Information and Spacetime Structure (I V Volovich)On Gaussian and Poisson White Noises (N Asai)Renormalization, Orthogonalization, and Generating Functions (N Asai et al.)Insider Trading in Continuous Time (E Barucci et al.)Existence, Uniqueness, Consistency and Dependency on Diffusion Coefficients of Generalized Solutions of Nonlinear Diffusion Equations in Colombeau's Algebra (H Deguchi)On Mathematical Treatment of Quantum Communication Gate on Fock Space (W Freudenberg et al.)A Frontier of White Noise Analysis (T Hida)An Interacting Fock Space with Periodic Jacobi Parameter Obtained from Regular Graphs in Large Scale Limit (A Hora & N Obata)Error Exponents of Codings for Stationary Gaussian Channels (S Ihara)White Noise Analysis on Classical Wiener Space Revisited (Y-J Lee & H-H Shih)Fractional Brownian Motions and the Lévy Laplacian (K Nishi et al.)Jump Finding of a Stable Process (Si Si et al.)On Entropy Production of a One-Dimensional Lattice Conductor (S Tasaki) Readership: Researchers in probability & statistics, mathematical physics, functional analysis and mathematical biology. Keywords:Quantum Information;White Noise Analysis;Fock Space;Classical Wiener Space;Brownian Motion