Stochastic Processes And Functional Analysis
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Stochastic Processes And Functional Analysis
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Author : Alan C. Krinik
language : en
Publisher: CRC Press
Release Date : 2004-03-23
Stochastic Processes And Functional Analysis written by Alan C. Krinik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-23 with Mathematics categories.
This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes, as made manifest in M. M. Rao's prolific research achievements. Featuring a biography of M. M. Rao, a complete bibliography of his published works, and meditations from former students, the book includes contributions from over 30 notable researchers.
Functional Analysis For Probability And Stochastic Processes
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Author : Adam Bobrowski
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-11
Functional Analysis For Probability And Stochastic Processes written by Adam Bobrowski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-11 with Mathematics categories.
This text presents selected areas of functional analysis that can facilitate an understanding of ideas in probability and stochastic processes. Topics covered include basic Hilbert and Banach spaces, weak topologies and Banach algebras, and the theory ofsemigroups of bounded linear operators.
Stochastic Processes And Functional Analysis
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Author : Alan C. Krinik
language : en
Publisher: CRC Press
Release Date : 2004-03-23
Stochastic Processes And Functional Analysis written by Alan C. Krinik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-23 with Mathematics categories.
This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochas
Stochastic Processes And Functional Analysis
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Author : Randall J. Swift
language : en
Publisher: American Mathematical Society
Release Date : 2021-11-22
Stochastic Processes And Functional Analysis written by Randall J. Swift and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Celebrating M. M. Rao's Many Mathematical Contributions as he Turns 90 Years Old, held from November 9–10, 2019, at the University of California, Riverside, California. The articles show the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes and their applications. The volume also includes a biography of M. M. Rao and the list of his publications.
Functional Analysis For Probability And Stochastic Processes
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Author : Adam Bobrowski
language : en
Publisher:
Release Date : 2005
Functional Analysis For Probability And Stochastic Processes written by Adam Bobrowski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Functional analysis categories.
This text is designed both for students of probability and stochastic processes, and for students of functional analysis. Numerous standard and non-standard examples and exercises make it suitable for both a textbook for a course as well as for self-study.
Introduction To Infinite Dimensional Stochastic Analysis
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Author : Zhi-yuan Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang 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 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).
Stochastic Processes And Functional Analysis
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Author : Jerome Goldstein
language : en
Publisher: CRC Press
Release Date : 1997-01-02
Stochastic Processes And Functional Analysis written by Jerome Goldstein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-02 with Mathematics categories.
"Covers the areas of modern analysis and probability theory. Presents a collection of papers given at the Festschrift held in honor of the 65 birthday of M. M. Rao, whose prolific published research includes the well-received Marcel Dekker, Inc. books Theory of Orlicz Spaces and Conditional Measures and Applications. Features previously unpublished research articles by a host of internationally recognized scholars."
Semiclassical Analysis For Diffusions And Stochastic Processes
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Author : Vassili N. Kolokoltsov
language : en
Publisher: Springer
Release Date : 2007-12-03
Semiclassical Analysis For Diffusions And Stochastic Processes written by Vassili N. Kolokoltsov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-03 with Mathematics categories.
The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.
Stochastic Analysis In Discrete And Continuous Settings
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Author : Nicolas Privault
language : en
Publisher: Springer
Release Date : 2009-07-14
Stochastic Analysis In Discrete And Continuous Settings written by Nicolas Privault and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-14 with Mathematics categories.
This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.
Fourier Analysis And Stochastic Processes
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Author : Pierre Brémaud
language : en
Publisher: Springer
Release Date : 2014-09-16
Fourier Analysis And Stochastic Processes written by Pierre Brémaud and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-16 with Mathematics categories.
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). Each chapter has an exercise section, which makes Fourier Analysis and Stochastic Processes suitable for a graduate course in applied mathematics, as well as for self-study.