Stochastic Processes And Orthogonal Polynomials

Author : Wim Schoutens
Publisher : Springer Science & Business Media
Page : 170 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211709

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Stochastic Processes and Orthogonal Polynomials by Wim Schoutens Pdf

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.

Author : Manuel Domínguez de la Iglesia
Publisher : Cambridge University Press
Page : 348 pages
File Size : 40,8 Mb
Release : 2021-10-21
Category : Mathematics
ISBN : 9781009035200

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Orthogonal Polynomials in the Spectral Analysis of Markov Processes by Manuel Domínguez de la Iglesia Pdf

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.

Author : R. D. Cooper,Michael Rand Hoare,M. Rahman,Carleton University. Department of Mathematics
Publisher : Unknown
Page : 112 pages
File Size : 45,7 Mb
Release : 1975
Category : Functions, Special
ISBN : LCCN:77363671

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Stochastic Processes and Special Functions by R. D. Cooper,Michael Rand Hoare,M. Rahman,Carleton University. Department of Mathematics Pdf

Author : Shai M. J. Haran
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 52,7 Mb
Release : 2008-04-25
Category : Mathematics
ISBN : 9783540783787

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Arithmetical Investigations by Shai M. J. Haran Pdf

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.

Author : Giovanni Peccati,Murad S. Taqqu
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 52,5 Mb
Release : 2011-04-06
Category : Mathematics
ISBN : 9788847016798

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Wiener Chaos: Moments, Cumulants and Diagrams by Giovanni Peccati,Murad S. Taqqu Pdf

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.

Author : K Farahmand
Publisher : CRC Press
Page : 180 pages
File Size : 54,9 Mb
Release : 1998-08-15
Category : Mathematics
ISBN : 0582356229

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Topics in Random Polynomials by K Farahmand Pdf

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.

Author : Rainer Buckdahn,Hans J. Engelbert,Marc Yor
Publisher : CRC Press
Page : 296 pages
File Size : 47,9 Mb
Release : 2002-05-16
Category : Mathematics
ISBN : 9781482265231

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Stochastic Processes and Related Topics by Rainer Buckdahn,Hans J. Engelbert,Marc Yor Pdf

This volume comprises selected papers presented at the 12th Winter School on Stochastic Processes and their Applications, which was held in Siegmundsburg, Germany, in March 2000. The contents include Backward Stochastic Differential Equations; Semilinear PDE and SPDE; Arbitrage Theory; Credit Derivatives and Models for Correlated Defaults; Three In

Author : Shai M. J. Haran
Publisher : Springer
Page : 0 pages
File Size : 42,9 Mb
Release : 2008-05-02
Category : Mathematics
ISBN : 3540783784

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Arithmetical Investigations by Shai M. J. Haran Pdf

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.

Author : Francisco Marcellàn
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 55,5 Mb
Release : 2006-06-19
Category : Mathematics
ISBN : 9783540310624

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Orthogonal Polynomials and Special Functions by Francisco Marcellàn Pdf

Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.

Author : Christos Christopoulos
Publisher : CRC Press
Page : 658 pages
File Size : 52,6 Mb
Release : 2022-07-14
Category : Technology & Engineering
ISBN : 9781000631784

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Principles and Techniques of Electromagnetic Compatibility by Christos Christopoulos Pdf

This book provides a sound grasp of the fundamental concepts, applications, and practice of EMC. Developments in recent years have resulted in further increases in electrical component density, wider penetration of wireless technologies, and a significant increase in complexity of electrical and electronic equipment. New materials, which can be customized to meet EMC needs, have been introduced. Considerable progress has been made in developing numerical tools for complete system EMC simulation. EMC is now a central consideration in all industrial sectors. Maintaining the holistic approach of the previous edition of Principles and Techniques of Electromagnetic Compatibility, the Third Edition updates coverage of EMC to reflects recent important developments. What is new in the Third Edition? A comprehensive treatment of new materials (meta- and nano-) and their impact on EMC Numerical modelling of complex systems and complexity reduction methods Impact of wireless technologies and the Internet of Things (IoT) on EMC Testing in reverberation chambers, and in the time-domain A comprehensive treatment of the scope and development of stochastic models for EMC EMC issues encountered in automotive, railway, aerospace, and marine applications Impact of EMC and Intentional EMI (IEMI) on infrastructure, and risk assessment In addition to updating material, new references, examples, and appendices were added to offer further support to readers interested in exploring further. As in previous editions, the emphasis is on building a sound theoretical framework, and demonstrating how it can be turned to practical use in challenging applications. The expectation is that this approach will serve EMC engineers through the inevitable future technological shifts and developments.

Author : Richard Bellman
Publisher : American Mathematical Soc.
Page : 328 pages
File Size : 49,7 Mb
Release : 1964
Category : Engineering mathematics
ISBN : 9780821813164

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Stochastic Processes in Mathematical Physics and Engineering by Richard Bellman Pdf

Author : Stephen A. Hambric,Shung H. Sung,Donald J. Nefske
Publisher : John Wiley & Sons
Page : 536 pages
File Size : 40,8 Mb
Release : 2016-05-02
Category : Technology & Engineering
ISBN : 9781119953449

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Engineering Vibroacoustic Analysis by Stephen A. Hambric,Shung H. Sung,Donald J. Nefske Pdf

The book describes analytical methods (based primarily on classical modal synthesis), the Finite Element Method (FEM), Boundary Element Method (BEM), Statistical Energy Analysis (SEA), Energy Finite Element Analysis (EFEA), Hybrid Methods (FEM-SEA and Transfer Path Analysis), and Wave-Based Methods. The book also includes procedures for designing noise and vibration control treatments, optimizing structures for reduced vibration and noise, and estimating the uncertainties in analysis results. Written by several well-known authors, each chapter includes theoretical formulations, along with practical applications to actual structural-acoustic systems. Readers will learn how to use vibroacoustic analysis methods in product design and development; how to perform transient, frequency (deterministic and random), and statistical vibroacoustic analyses; and how to choose appropriate structural and acoustic computational methods for their applications. The book can be used as a general reference for practicing engineers, or as a text for a technical short course or graduate course.

Author : Andrei N Borodin
Publisher : Birkhäuser
Page : 626 pages
File Size : 42,9 Mb
Release : 2017-10-30
Category : Mathematics
ISBN : 9783319623108

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Stochastic Processes by Andrei N Borodin Pdf

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.

Author : Emanuel Parzen
Publisher : SIAM
Page : 339 pages
File Size : 47,5 Mb
Release : 1999-12-01
Category : Mathematics
ISBN : 9780898714418

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Stochastic Processes by Emanuel Parzen Pdf

Ideal for courses aiming to give examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models. It introduces the methods of probability model building and provides the reader with mathematically sound techniques as well as the ability to further study the theory of stochastic processes.

Author : Akihito Hora,Nobuaki Obata
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 46,8 Mb
Release : 2007-07-05
Category : Science
ISBN : 9783540488637

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Quantum Probability and Spectral Analysis of Graphs by Akihito Hora,Nobuaki Obata Pdf

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.