Stochastic Processes And Orthogonal Polynomials

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Stochastic Processes and Orthogonal Polynomials

Author : Wim Schoutens
Publisher : Springer Science & Business Media
ISBN 13 : 1461211700
Total Pages : 170 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stochastic Processes and Orthogonal Polynomials by : Wim Schoutens

Download or read book Stochastic Processes and Orthogonal Polynomials written by Wim Schoutens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers an accessible reference for researchers in the probability, statistics and special functions communities. It gives a variety of interdisciplinary relations between the two main ingredients of stochastic processes and orthogonal polynomials. It covers topics like time dependent and asymptotic analysis for birth-death processes and diffusions, martingale relations for Lévy processes, stochastic integrals and Stein's approximation method. Almost all well-known orthogonal polynomials, which are brought together in the so-called Askey Scheme, come into play. This volume clearly illustrates the powerful mathematical role of orthogonal polynomials in the analysis of stochastic processes and is made accessible for all mathematicians with a basic background in probability theory and mathematical analysis. Wim Schoutens is a Postdoctoral Researcher of the Fund for Scientific Research-Flanders (Belgium). He received his PhD in Science from the Catholic University of Leuven, Belgium.

Orthogonal Polynomials in the Spectral Analysis of Markov Processes

Author : Manuel Domínguez de la Iglesia
Publisher : Cambridge University Press
ISBN 13 : 1009035207
Total Pages : 348 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Orthogonal Polynomials in the Spectral Analysis of Markov Processes by : Manuel Domínguez de la Iglesia

Download or read book Orthogonal Polynomials in the Spectral Analysis of Markov Processes written by Manuel Domínguez de la Iglesia and published by Cambridge University Press. This book was released on 2021-10-21 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In pioneering work in the 1950s, S. Karlin and J. McGregor showed that probabilistic aspects of certain Markov processes can be studied by analyzing orthogonal eigenfunctions of associated operators. In the decades since, many authors have extended and deepened this surprising connection between orthogonal polynomials and stochastic processes. This book gives a comprehensive analysis of the spectral representation of the most important one-dimensional Markov processes, namely discrete-time birth-death chains, birth-death processes and diffusion processes. It brings together the main results from the extensive literature on the topic with detailed examples and applications. Also featuring an introduction to the basic theory of orthogonal polynomials and a selection of exercises at the end of each chapter, it is suitable for graduate students with a solid background in stochastic processes as well as researchers in orthogonal polynomials and special functions who want to learn about applications of their work to probability.

Stochastic Processes and Special Functions

Author : R. D. Cooper
Publisher :
ISBN 13 :
Total Pages : 112 pages
Book Rating : 4.:/5 (773 download)

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Book Synopsis Stochastic Processes and Special Functions by : R. D. Cooper

Download or read book Stochastic Processes and Special Functions written by R. D. Cooper and published by . This book was released on 1975 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Arithmetical Investigations

Author : Shai M. J. Haran
Publisher : Springer Science & Business Media
ISBN 13 : 3540783784
Total Pages : 224 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Arithmetical Investigations by : Shai M. J. Haran

Download or read book Arithmetical Investigations written by Shai M. J. Haran and published by Springer Science & Business Media. This book was released on 2008-04-25 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.

Wiener Chaos: Moments, Cumulants and Diagrams

Author : Giovanni Peccati
Publisher : Springer Science & Business Media
ISBN 13 : 8847016797
Total Pages : 281 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Wiener Chaos: Moments, Cumulants and Diagrams by : Giovanni Peccati

Download or read book Wiener Chaos: Moments, Cumulants and Diagrams written by Giovanni Peccati and published by Springer Science & Business Media. This book was released on 2011-04-06 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of orthogonal polynomials associated with probability distributions on the real line. It plays a crucial role in modern probability theory, with applications ranging from Malliavin calculus to stochastic differential equations and from probabilistic approximations to mathematical finance. This book is concerned with combinatorial structures arising from the study of chaotic random variables related to infinitely divisible random measures. The combinatorial structures involved are those of partitions of finite sets, over which Möbius functions and related inversion formulae are defined. This combinatorial standpoint (which is originally due to Rota and Wallstrom) provides an ideal framework for diagrams, which are graphical devices used to compute moments and cumulants of random variables. Several applications are described, in particular, recent limit theorems for chaotic random variables. An Appendix presents a computer implementation in MATHEMATICA for many of the formulae.

Topics in Random Polynomials

Author : K Farahmand
Publisher : CRC Press
ISBN 13 : 9780582356221
Total Pages : 180 pages
Book Rating : 4.3/5 (562 download)

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Book Synopsis Topics in Random Polynomials by : K Farahmand

Download or read book Topics in Random Polynomials written by K Farahmand and published by CRC Press. This book was released on 1998-08-15 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Random Polynomials presents a rigorous and comprehensive treatment of the mathematical behavior of different types of random polynomials. These polynomials-the subject of extensive recent research-have many applications in physics, economics, and statistics. The main results are presented in such a fashion that they can be understood and used by readers whose knowledge of probability incorporates little more than basic probability theory and stochastic processes.

Arithmetical Investigations

Author : Shai M. J. Haran
Publisher : Springer
ISBN 13 : 9783540783787
Total Pages : 0 pages
Book Rating : 4.7/5 (837 download)

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Book Synopsis Arithmetical Investigations by : Shai M. J. Haran

Download or read book Arithmetical Investigations written by Shai M. J. Haran and published by Springer. This book was released on 2008-05-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.

Stochastic Processes

Author : Jyotiprasad Medhi
Publisher : New Age International
ISBN 13 : 9788122405491
Total Pages : 664 pages
Book Rating : 4.4/5 (54 download)

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Book Synopsis Stochastic Processes by : Jyotiprasad Medhi

Download or read book Stochastic Processes written by Jyotiprasad Medhi and published by New Age International. This book was released on 1994 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims At The Level Between That Of Elementary Probability Texts And Advanced Works On Stochastic Processes. The Pre-Requisites Are A Course On Elementary Probability Theory And Statistics, And A Course On Advanced Calculus. The Theoretical Results Developed Have Been Followed By A Large Number Of Illustrative Examples. These Have Been Supplemented By Numerous Exercises, Answers To Most Of Which Are Also Given. It Will Suit As A Text For Advanced Undergraduate, Postgraduate And Research Level Course In Applied Mathematics, Statistics, Operations Research, Computer Science, Different Branches Of Engineering, Telecommunications, Business And Management, Economics, Life Sciences And So On. A Review Of The Book In American Mathematical Monthly (December 82) Gives This Book Special Positive Emphasis As A Textbook As Follows: 'Of The Dozen Or More Texts Published In The Last Five Years Aimed At The Students With A Background Of A First Course In Probability And Statistics But Not Yet To Measure Theory, This Is The Clear Choice. An Extremely Well Organized, Lucidly Written Text With Numerous Problems, Examples And Reference T* (With T* Where T Denotes Textbook And * Denotes Special Positive Emphasis). The Current Enlarged And Revised Edition, While Retaining The Structure And Adhering To The Objective As Well As Philosophy Of The Earlier Edition, Removes The Deficiencies, Updates The Material And The References And Aims At A Border Perspective With Substantial Additions And Wider Coverage.

Stochastic Processes

Author : Andrei N Borodin
Publisher : Birkhäuser
ISBN 13 : 3319623109
Total Pages : 641 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Stochastic Processes by : Andrei N Borodin

Download or read book Stochastic Processes written by Andrei N Borodin and published by Birkhäuser. This book was released on 2017-10-30 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations

Author :
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations by :

Download or read book The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations written by and published by . This book was released on 2003 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new method for solving stochastic differential equations based on Galerking projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte-Carlo simulations for low dimensional stochastic inputs.

Stochastic Monotonicity and Queueing Applications of Birth-Death Processes

Author : Erik van Doorn
Publisher : Springer Science & Business Media
ISBN 13 : 1461258839
Total Pages : 125 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stochastic Monotonicity and Queueing Applications of Birth-Death Processes by : Erik van Doorn

Download or read book Stochastic Monotonicity and Queueing Applications of Birth-Death Processes written by Erik van Doorn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: A stochastic process {X(t): 0 S t =} with discrete state space S c ~ is said to be stochastically increasing (decreasing) on an interval T if the probabilities Pr{X(t) i}, i E S, are increasing (decreasing) with t on T. Stochastic monotonicity is a basic structural property for process behaviour. It gives rise to meaningful bounds for various quantities such as the moments of the process, and provides the mathematical groundwork for approximation algorithms. Obviously, stochastic monotonicity becomes a more tractable subject for analysis if the processes under consideration are such that stochastic mono tonicity on an inter val 0

Extrapolation and Rational Approximation

Author : Claude Brezinski
Publisher : Springer Nature
ISBN 13 : 3030584186
Total Pages : 410 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Extrapolation and Rational Approximation by : Claude Brezinski

Download or read book Extrapolation and Rational Approximation written by Claude Brezinski and published by Springer Nature. This book was released on 2020-11-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Padé approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects. A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the “actors.” This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.

Stochastic Processes and Random Matrices

Author : Gregory Schehr
Publisher : Oxford University Press
ISBN 13 : 0198797311
Total Pages : 641 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Stochastic Processes and Random Matrices by : Gregory Schehr

Download or read book Stochastic Processes and Random Matrices written by Gregory Schehr and published by Oxford University Press. This book was released on 2017 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers in detail recent developments in the field of stochastic processes and Random Matrix Theory. Matrix models have been playing an important role in theoretical physics for a long time and are currently also a very active domain of research in mathematics.

Lévy Processes

Author : Ole E Barndorff-Nielsen
Publisher : Springer Science & Business Media
ISBN 13 : 1461201977
Total Pages : 414 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Lévy Processes by : Ole E Barndorff-Nielsen

Download or read book Lévy Processes written by Ole E Barndorff-Nielsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.

Malliavin Calculus for Lévy Processes with Applications to Finance

Author : Giulia Di Nunno
Publisher : Springer Science & Business Media
ISBN 13 : 3540785728
Total Pages : 421 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Malliavin Calculus for Lévy Processes with Applications to Finance by : Giulia Di Nunno

Download or read book Malliavin Calculus for Lévy Processes with Applications to Finance written by Giulia Di Nunno and published by Springer Science & Business Media. This book was released on 2008-10-08 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.

Computational Aspects of Linear Control

Author : Claude Brezinski
Publisher : Springer Science & Business Media
ISBN 13 : 1461302617
Total Pages : 296 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Computational Aspects of Linear Control by : Claude Brezinski

Download or read book Computational Aspects of Linear Control written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed. The problem is to regulate the input in order to control the output, that is for obtaining a desired output. Such a mechanism, where the input is modified according to the output measured, is called feedback. The study and design of such automatic processes is called control theory. As we will see, the term system embraces any device and control theory has a wide variety of applications in the real world. Control theory is an interdisci plinary domain at the junction of differential and difference equations, system theory and statistics. Moreover, the solution of a control problem involves many topics of numerical analysis and leads to many interesting computational problems: linear algebra (QR, SVD, projections, Schur complement, structured matrices, localization of eigenvalues, computation of the rank, Jordan normal form, Sylvester and other equations, systems of linear equations, regulariza tion, etc), root localization for polynomials, inversion of the Laplace transform, computation of the matrix exponential, approximation theory (orthogonal poly nomials, Pad6 approximation, continued fractions and linear fractional transfor mations), optimization, least squares, dynamic programming, etc. So, control theory is also a. good excuse for presenting various (sometimes unrelated) issues of numerical analysis and the procedures for their solution. This book is not a book on control.

Quantum Probability and Spectral Analysis of Graphs

Author : Akihito Hora
Publisher : Springer Science & Business Media
ISBN 13 : 3540488634
Total Pages : 384 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Quantum Probability and Spectral Analysis of Graphs by : Akihito Hora

Download or read book Quantum Probability and Spectral Analysis of Graphs written by Akihito Hora and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.