Fourier Analysis and Stochastic Processes
Fourier Analysis and Stochastic Processes

Author: Pierre Brémaud

Publisher: Springer

Published: 2014-09-16

Total Pages: 396

ISBN-13: 3319095900

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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.

Stationary Stochastic Processes for Scientists and Engineers
Stationary Stochastic Processes for Scientists and Engineers

Author: Georg Lindgren

Publisher: CRC Press

Published: 2013-10-11

Total Pages: 316

ISBN-13: 1466586192

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Suitable for a one-semester course, this text teaches students how to use stochastic processes efficiently. Carefully balancing mathematical rigor and ease of exposition, the book provides students with a sufficient understanding of the theory and a practical appreciation of how it is used in real-life situations. Special emphasis is on the interpretation of various statistical models and concepts as well as the types of questions statistical analysis can answer. To enable hands-on practice, MATLAB code is available online.

Stochastic Processes and Applications
Stochastic Processes and Applications

Author: Grigorios A. Pavliotis

Publisher: Springer

Published: 2014-11-19

Total Pages: 345

ISBN-13: 1493913239

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This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

Upper and Lower Bounds for Stochastic Processes
Upper and Lower Bounds for Stochastic Processes

Author: Michel Talagrand

Publisher: Springer Science & Business Media

Published: 2014-02-12

Total Pages: 630

ISBN-13: 3642540759

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The book develops modern methods and in particular the "generic chaining" to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes. Applications are given to stable processes, infinitely divisible processes, matching theorems, the convergence of random Fourier series, of orthogonal series, and to functional analysis. The complete solution of a number of classical problems is given in complete detail, and an ambitious program for future research is laid out.

Harmonic Analysis and the Theory of Probability
Harmonic Analysis and the Theory of Probability

Author: Saloman Bochner

Publisher: Univ of California Press

Published: 2023-11-15

Total Pages: 184

ISBN-13: 0520345290

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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.

Theory of Martingales
Theory of Martingales

Author: Robert Liptser

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 806

ISBN-13: 9400924380

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One service mathematics has rc:ndered the 'Et moi, "', si j'avait su comment CD revenir, je n'y serais point alle. ' human race. It has put common SCIIJC back Jules Verne where it belongs. on the topmost shelf next to tbe dusty canister 1abdled 'discarded non- The series is divergent; tberefore we may be sense'. able to do sometbing witb it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science ... '; 'One service category theory has rendered mathematics ... '. All arguably true_ And all statements obtainable this way form part of the raison d'etre of this series_ This series, Mathematics and Its ApplicatiOns, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope_ At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches.

Applied Stochastic Differential Equations
Applied Stochastic Differential Equations

Author: Simo Särkkä

Publisher: Cambridge University Press

Published: 2019-05-02

Total Pages: 327

ISBN-13: 1316510085

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With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Fourier Analysis in Probability Theory
Fourier Analysis in Probability Theory

Author: Tatsuo Kawata

Publisher: Academic Press

Published: 2014-06-17

Total Pages: 681

ISBN-13: 148321852X

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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.