Introduction To Hida Distributions

Author : Si Si
Publisher : World Scientific
ISBN 13 : 9812836888
Total Pages : 268 pages
Book Rating : 4.85/5 ( download)

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Download or read book Introduction to Hida Distributions written by Si Si and published by World Scientific. This book was released on 2012 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the mathematical definition of white noise and gives its significance. White noise is in fact a typical class of idealized elemental (infinitesimal) random variables. Thus, we are naturally led to have functionals of such elemental random variables that is white noise. This book analyzes those functionals of white noise, particularly the generalized ones called Hida distributions, and highlights some interesting future directions. The main part of the book involves infinite dimensional differential and integral calculus based on the variable which is white noise.The present book can be used as a supplementary book to Lectures on White Noise Functionals published in 2008, with detailed background provided.

Author : Zhi-yuan Huang
Publisher : Springer Science & Business Media
ISBN 13 : 9401141088
Total Pages : 308 pages
Book Rating : 4.86/5 ( download)

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Download or read book Introduction to Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. The stochastic analysis created by K. Ito (also independently by Gihman [1]) in the forties is essentially an infinitesimal analysis for trajectories of stochastic processes. By virtue of Ito's stochastic differential equations one can construct diffusion processes via direct probabilistic methods and treat them as function als of Brownian paths (i. e. the Wiener functionals).

Author : Richard Phillips Feynman
Publisher : World Scientific
ISBN 13 : 9812560645
Total Pages : 313 pages
Book Rating : 4.43/5 ( download)

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Download or read book Stochastic Analysis and Mathematical Physics (SAMP/ANESTOC 2002) written by Richard Phillips Feynman and published by World Scientific. This book was released on 2004 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects a series of papers centered on two main streams: Feynman path integral approach to Quantum Mechanics and statistical mechanics of quantum open systems. Key authors discuss the state-of-the-art within their fields of expertise. In addition, the volume includes a number of contributed papers with new results, which have been thoroughly refereed.The contributions in this volume highlight emergent research in the area of stochastic analysis and mathematical physics, focusing, in particular on Feynman functional integral approach and, on the other hand, in quantum probability. The book is addressed to an audience of mathematical physicists, as well as specialists in probability theory, stochastic analysis and operator algebras.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences

Author : Robert C. Dalang
Publisher : Birkhäuser
ISBN 13 : 3034809093
Total Pages : 402 pages
Book Rating : 4.92/5 ( download)

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Download or read book Stochastic Analysis: A Series of Lectures written by Robert C. Dalang and published by Birkhäuser. This book was released on 2015-07-28 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author :
Publisher :
ISBN 13 :
Total Pages : 760 pages
Book Rating : 4.87/5 ( download)

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Download or read book Ricerche di matematica written by and published by . This book was released on 2012 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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Publisher :
ISBN 13 :
Total Pages : 1884 pages
Book Rating : 4.58/5 ( download)

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Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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ISBN 13 :
Total Pages : 562 pages
Book Rating : 4.76/5 ( download)

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Download or read book 数理科学講究錄 written by and published by . This book was released on 1996 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : L.M. Ricciardi
Publisher : American Institute of Physics
ISBN 13 : 9780735405523
Total Pages : 386 pages
Book Rating : 4.22/5 ( download)

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Download or read book Collective Dynamics: Topics on Competition and Cooperation in the Biosciences written by L.M. Ricciardi and published by American Institute of Physics. This book was released on 2008-07-16 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: All papers have been peer-reviewed. The Conference was a program of invited lectures and selected contributed papers of interest to academic communities, educators and students both at graduate and undergraduate levels. Topics are centered on information processing and coding in the brain and in neuronal systems, on quantitative approaches to ecology and population dynamics, and on bioinformatics. Some talks also focus on current problems in various other areas of applications of mathematics and computational tools to the life sciences.

Author : Paul Malliavin
Publisher : Springer Science & Business Media
ISBN 13 : 3540307990
Total Pages : 148 pages
Book Rating : 4.90/5 ( download)

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Download or read book Stochastic Calculus of Variations in Mathematical Finance written by Paul Malliavin and published by Springer Science & Business Media. This book was released on 2006-02-25 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highly esteemed author Topics covered are relevant and timely

Author : Hida Takeyuki
Publisher : World Scientific
ISBN 13 : 9813220953
Total Pages : 232 pages
Book Rating : 4.59/5 ( download)

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Download or read book Let Us Use White Noise written by Hida Takeyuki and published by World Scientific. This book was released on 2017-03-10 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why should we use white noise analysis? Well, one reason of course is that it fills that earlier gap in the tool kit. As Hida would put it, white noise provides us with a useful set of independent coordinates, parametrized by "time". And there is a feature which makes white noise analysis extremely user-friendly. Typically the physicist — and not only he — sits there with some heuristic ansatz, like e.g. the famous Feynman "integral", wondering whether and how this might make sense mathematically. In many cases the characterization theorem of white noise analysis provides the user with a sweet and easy answer. Feynman's "integral" can now be understood, the "It's all in the vacuum" ansatz of Haag and Coester is now making sense via Dirichlet forms, and so on in many fields of application. There is mathematical finance, there have been applications in biology, and engineering, many more than we could collect in the present volume. Finally, there is one extra benefit: when we internalize the structures of Gaussian white noise analysis we will be ready to meet another close relative. We will enjoy the important similarities and differences which we encounter in the Poisson case, championed in particular by Y Kondratiev and his group. Let us look forward to a companion volume on the uses of Poisson white noise. The present volume is more than a collection of autonomous contributions. The introductory chapter on white noise analysis was made available to the other authors early on for reference and to facilitate conceptual and notational coherence in their work.