Fourier Analysis in Probability Theory PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Fourier Analysis in Probability Theory PDF full book. Access full book title Fourier Analysis in Probability Theory by Tatsuo Kawata. Download full books in PDF and EPUB format.
Author: Tatsuo Kawata Publisher: Academic Press ISBN: 148321852X Category : Mathematics Languages : en Pages : 681
Book Description
Fourier Analysis in Probability Theory provides useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related studies. This 14-chapter work highlights the clarification of the interactions and analogies among these theories. Chapters 1 to 8 present the elements of classical Fourier analysis, in the context of their applications to probability theory. Chapters 9 to 14 are devoted to basic results from the theory of characteristic functions of probability distributors, the convergence of distribution functions in terms of characteristic functions, and series of independent random variables. This book will be of value to mathematicians, engineers, teachers, and students.
Author: Tatsuo Kawata Publisher: Academic Press ISBN: 148321852X Category : Mathematics Languages : en Pages : 681
Book Description
Fourier Analysis in Probability Theory provides useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related studies. This 14-chapter work highlights the clarification of the interactions and analogies among these theories. Chapters 1 to 8 present the elements of classical Fourier analysis, in the context of their applications to probability theory. Chapters 9 to 14 are devoted to basic results from the theory of characteristic functions of probability distributors, the convergence of distribution functions in terms of characteristic functions, and series of independent random variables. This book will be of value to mathematicians, engineers, teachers, and students.
Author: Saloman Bochner Publisher: Univ of California Press ISBN: 0520345290 Category : Mathematics Languages : en Pages : 184
Book Description
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.
Author: Pierre Brémaud Publisher: Springer ISBN: 3319095900 Category : Mathematics Languages : en Pages : 396
Book Description
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.
Author: John J. Benedetto Publisher: CRC Press ISBN: 1000674150 Category : Mathematics Languages : en Pages : 668
Book Description
The Journal of Fourier Analysis and Applications is a journal of the mathematical sciences devoted to Fourier analysis and its applications. The subject of Fourier analysis has had a major impact on the development of mathematics, on the understanding of many engineering and scientific phenomena, and on the solution of some of the most important problems in mathematics and the sciences. At the end of June 1993, a large Conference in Harmonic Analysis was held at the University of Paris-Sud at Orsay to celebrate the prominent role played by Jean-Pierre Kahane and his numerous achievements in this field. The large variety of topics discussed in this meeting, ranging from classical Harmonic Analysis to Probability Theory, reflects the intense mathematical curiosity and the broad mathematical interest of Jean-Pierre Kahane. Indeed, all of them are connected to his work. The mornings were devoted to plenary addresses while up to four parallel sessions took place in the afternoons. Altogether, there were about eighty speakers. This wide range of subjects appears in these proceedings which include thirty six articles.
Author: Saloman Bochner Publisher: Univ of California Press ISBN: 0520345282 Category : Mathematics Languages : en Pages : 184
Book Description
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.
Author: Elias M. Stein Publisher: Princeton University Press ISBN: 1400831237 Category : Mathematics Languages : en Pages : 326
Book Description
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Author: Herbert Heyer Publisher: World Scientific ISBN: 9814282480 Category : Mathematics Languages : en Pages : 425
Book Description
The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation ? the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups ? is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm?Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.
Author: Malcolm Adams Publisher: Springer Science & Business Media ISBN: 1461207797 Category : Mathematics Languages : en Pages : 217
Book Description
"...the text is user friendly to the topics it considers and should be very accessible...Instructors and students of statistical measure theoretic courses will appreciate the numerous informative exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association
Author: Tatsuo Kawata
Author: Tatsuo Kawata
Author: TATSUO. KAWATA
Author: Saloman Bochner
Author: Pierre Brémaud
Author: John J. Benedetto
Author: Saloman Bochner
Author: Elias M. Stein
Author: Audrey Terras
Author: Herbert Heyer
Author: Malcolm Adams