Wiener Chaos Moments Cumulants And Diagrams

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Wiener Chaos: Moments, Cumulants and Diagrams

Giovanni Peccati,Murad S. Taqqu
Wiener Chaos Moments Cumulants and Diagrams Book PDF

Author : Giovanni Peccati,Murad S. Taqqu
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 48,7 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.

Stochastic Analysis for Poisson Point Processes

Giovanni Peccati,Matthias Reitzner
Stochastic Analysis for Poisson Point Processes Book PDF

Author : Giovanni Peccati,Matthias Reitzner
Publisher : Springer
Page : 346 pages
File Size : 44,8 Mb
Release : 2016-07-07
Category : Mathematics
ISBN : 9783319052335

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Stochastic Analysis for Poisson Point Processes by Giovanni Peccati,Matthias Reitzner Pdf

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.

Classical Hopf Algebras and Their Applications

Pierre Cartier,Frédéric Patras
Classical Hopf Algebras and Their Applications Book PDF

Author : Pierre Cartier,Frédéric Patras
Publisher : Springer Nature
Page : 277 pages
File Size : 46,6 Mb
Release : 2021-09-20
Category : Mathematics
ISBN : 9783030778453

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Classical Hopf Algebras and Their Applications by Pierre Cartier,Frédéric Patras Pdf

This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s. The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results. Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras.

Geometry and Invariance in Stochastic Dynamics

Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger
Geometry and Invariance in Stochastic Dynamics Book PDF

Author : Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger
Publisher : Springer Nature
Page : 273 pages
File Size : 55,7 Mb
Release : 2022-02-09
Category : Mathematics
ISBN : 9783030874322

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Geometry and Invariance in Stochastic Dynamics by Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger Pdf

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.

In Memoriam Marc Yor - Séminaire de Probabilités XLVII

Catherine Donati-Martin,Antoine Lejay,Alain Rouault
In Memoriam Marc Yor S minaire de Probabilit s XLVII Book PDF

Author : Catherine Donati-Martin,Antoine Lejay,Alain Rouault
Publisher : Springer
Page : 619 pages
File Size : 53,5 Mb
Release : 2015-09-07
Category : Mathematics
ISBN : 9783319185859

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In Memoriam Marc Yor - Séminaire de Probabilités XLVII by Catherine Donati-Martin,Antoine Lejay,Alain Rouault Pdf

This volume is dedicated to the memory of Marc Yor, who passed away in 2014. The invited contributions by his collaborators and former students bear testament to the value and diversity of his work and of his research focus, which covered broad areas of probability theory. The volume also provides personal recollections about him, and an article on his essential role concerning the Doeblin documents. With contributions by P. Salminen, J-Y. Yen & M. Yor; J. Warren; T. Funaki; J. Pitman& W. Tang; J-F. Le Gall; L. Alili, P. Graczyk & T. Zak; K. Yano & Y. Yano; D. Bakry & O. Zribi; A. Aksamit, T. Choulli & M. Jeanblanc; J. Pitman; J. Obloj, P. Spoida & N. Touzi; P. Biane; J. Najnudel; P. Fitzsimmons, Y. Le Jan & J. Rosen; L.C.G. Rogers & M. Duembgen; E. Azmoodeh, G. Peccati & G. Poly, timP-L Méliot, A. Nikeghbali; P. Baldi; N. Demni, A. Rouault & M. Zani; N. O'Connell; N. Ikeda & H. Matsumoto; A. Comtet & Y. Tourigny; P. Bougerol; L. Chaumont; L. Devroye & G. Letac; D. Stroock and M. Emery.

Analysis of Variations for Self-similar Processes

Ciprian Tudor
Analysis of Variations for Self similar Processes Book PDF

Author : Ciprian Tudor
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 41,5 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9783319009360

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Analysis of Variations for Self-similar Processes by Ciprian Tudor Pdf

Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.

Séminaire de Probabilités XLV

Catherine Donati-Martin,Antoine Lejay,Alain Rouault
S minaire de Probabilit s XLV Book PDF

Author : Catherine Donati-Martin,Antoine Lejay,Alain Rouault
Publisher : Springer
Page : 558 pages
File Size : 46,9 Mb
Release : 2013-07-19
Category : Mathematics
ISBN : 9783319003214

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Séminaire de Probabilités XLV by Catherine Donati-Martin,Antoine Lejay,Alain Rouault Pdf

The series of advanced courses initiated in Séminaire de Probabilités XXXIII continues with a course by Ivan Nourdin on Gaussian approximations using Malliavin calculus. The Séminaire also occasionally publishes a series of contributions on a unifying subject; in this spirit, selected participants to the September 2011 Conference on Stochastic Filtrations, held in Strasbourg and organized by Michel Émery, have also contributed to the present volume. The rest of the work covers a wide range of topics, such as stochastic calculus and Markov processes, random matrices and free probability, and combinatorial optimization.

Stochastic Analysis and Related Topics

Fabrice Baudoin,Jonathon Peterson
Stochastic Analysis and Related Topics Book PDF

Author : Fabrice Baudoin,Jonathon Peterson
Publisher : Birkhäuser
Page : 221 pages
File Size : 48,9 Mb
Release : 2017-10-04
Category : Mathematics
ISBN : 9783319596716

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Stochastic Analysis and Related Topics by Fabrice Baudoin,Jonathon Peterson Pdf

The articles in this collection are a sampling of some of the research presented during the conference “Stochastic Analysis and Related Topics”, held in May of 2015 at Purdue University in honor of the 60th birthday of Rodrigo Bañuelos. A wide variety of topics in probability theory is covered in these proceedings, including heat kernel estimates, Malliavin calculus, rough paths differential equations, Lévy processes, Brownian motion on manifolds, and spin glasses, among other topics.

Seminar on Stochastic Analysis, Random Fields and Applications VII

Robert C. Dalang,Marco Dozzi,Francesco Russo
Seminar on Stochastic Analysis Random Fields and Applications VII Book PDF

Author : Robert C. Dalang,Marco Dozzi,Francesco Russo
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 46,7 Mb
Release : 2013-09-05
Category : Mathematics
ISBN : 9783034805452

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Seminar on Stochastic Analysis, Random Fields and Applications VII by Robert C. Dalang,Marco Dozzi,Francesco Russo Pdf

This volume contains refereed research or review articles presented at the 7th Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verità) in Ascona , Switzerland, in May 2011. The seminar focused mainly on: - stochastic (partial) differential equations, especially with jump processes, construction of solutions and approximations - Malliavin calculus and Stein methods, and other techniques in stochastic analysis, especially chaos representations and convergence, and applications to models of interacting particle systems - stochastic methods in financial models, especially models for power markets or for risk analysis, empirical estimation and approximation, stochastic control and optimal pricing. The book will be a valuable resource for researchers in stochastic analysis and for professionals interested in stochastic methods in finance.​

Lectures on Gaussian Processes

Mikhail Lifshits
Lectures on Gaussian Processes Book PDF

Author : Mikhail Lifshits
Publisher : Springer Science & Business Media
Page : 129 pages
File Size : 55,9 Mb
Release : 2012-01-13
Category : Mathematics
ISBN : 9783642249389

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Lectures on Gaussian Processes by Mikhail Lifshits Pdf

Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.​

Lectures on the Poisson Process

Günter Last,Mathew Penrose
Lectures on the Poisson Process Book PDF

Author : Günter Last,Mathew Penrose
Publisher : Cambridge University Press
Page : 315 pages
File Size : 50,7 Mb
Release : 2017-10-26
Category : Mathematics
ISBN : 9781107088016

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Lectures on the Poisson Process by Günter Last,Mathew Penrose Pdf

A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

Normal Approximations with Malliavin Calculus

Ivan Nourdin,Giovanni Peccati
Normal Approximations with Malliavin Calculus Book PDF

Author : Ivan Nourdin,Giovanni Peccati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 40,6 Mb
Release : 2012-05-10
Category : Mathematics
ISBN : 9781107017771

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Normal Approximations with Malliavin Calculus by Ivan Nourdin,Giovanni Peccati Pdf

This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.

Functionals of Multidimensional Diffusions with Applications to Finance

Jan Baldeaux,Eckhard Platen
Functionals of Multidimensional Diffusions with Applications to Finance Book PDF

Author : Jan Baldeaux,Eckhard Platen
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 46,5 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9783319007472

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Functionals of Multidimensional Diffusions with Applications to Finance by Jan Baldeaux,Eckhard Platen Pdf

This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.​

Quantum Fields and Processes

John Gough,Joachim Kupsch
Quantum Fields and Processes Book PDF

Author : John Gough,Joachim Kupsch
Publisher : Cambridge University Press
Page : 341 pages
File Size : 54,9 Mb
Release : 2018-04-12
Category : Mathematics
ISBN : 9781108416764

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Quantum Fields and Processes by John Gough,Joachim Kupsch Pdf

Do quantum field theory without Feynman diagrams! Use the combinatorics behind cumulants, correlations, Green's functions and quantum fields.

Stochastic Processes and Applications

Sergei Silvestrov,Anatoliy Malyarenko,Milica Rančić
Stochastic Processes and Applications Book PDF

Author : Sergei Silvestrov,Anatoliy Malyarenko,Milica Rančić
Publisher : Springer
Page : 475 pages
File Size : 50,6 Mb
Release : 2018-12-05
Category : Mathematics
ISBN : 9783030028251

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Stochastic Processes and Applications by Sergei Silvestrov,Anatoliy Malyarenko,Milica Rančić Pdf

This book highlights the latest advances in stochastic processes, probability theory, mathematical statistics, engineering mathematics and algebraic structures, focusing on mathematical models, structures, concepts, problems and computational methods and algorithms important in modern technology, engineering and natural sciences applications. It comprises selected, high-quality, refereed contributions from various large research communities in modern stochastic processes, algebraic structures and their interplay and applications. The chapters cover both theory and applications, illustrated by numerous figures, schemes, algorithms, tables and research results to help readers understand the material and develop new mathematical methods, concepts and computing applications in the future. Presenting new methods and results, reviews of cutting-edge research, and open problems and directions for future research, the book serves as a source of inspiration for a broad spectrum of researchers and research students in probability theory and mathematical statistics, applied algebraic structures, applied mathematics and other areas of mathematics and applications of mathematics. The book is based on selected contributions presented at the International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications” (SPAS2017) to mark Professor Dmitrii Silvestrov’s 70th birthday and his 50 years of fruitful service to mathematics, education and international cooperation, which was held at Mälardalen University in Västerås and Stockholm University, Sweden, in October 2017.