Wiener Chaos Moments Cumulants And Diagrams

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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.

Random Processes by Example

Author : Mikhail Lifshits
Publisher : World Scientific
ISBN 13 : 9814522295
Total Pages : 232 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Random Processes by Example by : Mikhail Lifshits

Download or read book Random Processes by Example written by Mikhail Lifshits and published by World Scientific. This book was released on 2014 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes. Next, it illustrates general concepts by handling a transparent but rich example of a OC teletraffic modelOCO. A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable L(r)vy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations. The reader will quickly become familiar with key concepts that form a language for many major probabilistic models of real world phenomena but are often neglected in more traditional courses of stochastic processes. Sample Chapter(s). Chapter 1: Preliminaries (367 KB). Contents: Preliminaries: Random Variables: A Summary; From Poisson to Stable Variables; Limit Theorems for Sums and Domains of Attraction; Random Vectors; Random Processes: Random Processes: Main Classes; Examples of Gaussian Random Processes; Random Measures and Stochastic Integrals; Limit Theorems for Poisson Integrals; L(r)vy Processes; Spectral Representations; Convergence of Random Processes; Teletraffic Models: A Model of Service System; Limit Theorems for the Workload; Micropulse Model; Spacial Extensions. Readership: Graduate students and researchers in probability & statist

Functionals of Multidimensional Diffusions with Applications to Finance

Author : Jan Baldeaux
Publisher : Springer Science & Business Media
ISBN 13 : 3319007475
Total Pages : 432 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Functionals of Multidimensional Diffusions with Applications to Finance by : Jan Baldeaux

Download or read book Functionals of Multidimensional Diffusions with Applications to Finance written by Jan Baldeaux and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : John Gough
Publisher : Cambridge University Press
ISBN 13 : 1108416764
Total Pages : 341 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Quantum Fields and Processes by : John Gough

Download or read book Quantum Fields and Processes written by John Gough and published by Cambridge University Press. This book was released on 2018-04-12 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do quantum field theory without Feynman diagrams! Use the combinatorics behind cumulants, correlations, Green's functions and quantum fields.

Stochastic Processes and Applications

Author : Sergei Silvestrov
Publisher : Springer
ISBN 13 : 3030028259
Total Pages : 482 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Stochastic Processes and Applications by : Sergei Silvestrov

Download or read book Stochastic Processes and Applications written by Sergei Silvestrov and published by Springer. This book was released on 2018-12-05 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Artificial Neural Networks and Machine Learning – ICANN 2020

Author : Igor Farkaš
Publisher : Springer Nature
ISBN 13 : 3030616096
Total Pages : 891 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Artificial Neural Networks and Machine Learning – ICANN 2020 by : Igor Farkaš

Download or read book Artificial Neural Networks and Machine Learning – ICANN 2020 written by Igor Farkaš and published by Springer Nature. This book was released on 2020-10-19 with total page 891 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings set LNCS 12396 and 12397 constitute the proceedings of the 29th International Conference on Artificial Neural Networks, ICANN 2020, held in Bratislava, Slovakia, in September 2020.* The total of 139 full papers presented in these proceedings was carefully reviewed and selected from 249 submissions. They were organized in 2 volumes focusing on topics such as adversarial machine learning, bioinformatics and biosignal analysis, cognitive models, neural network theory and information theoretic learning, and robotics and neural models of perception and action. *The conference was postponed to 2021 due to the COVID-19 pandemic.

Random Growth Models

Author : Michael Damron
Publisher : American Mathematical Soc.
ISBN 13 : 1470435535
Total Pages : 274 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Random Growth Models by : Michael Damron

Download or read book Random Growth Models written by Michael Damron and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA. The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.

Stochastic Analysis and Related Topics

Author : Fabrice Baudoin
Publisher : Birkhäuser
ISBN 13 : 3319596713
Total Pages : 224 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Stochastic Analysis and Related Topics by : Fabrice Baudoin

Download or read book Stochastic Analysis and Related Topics written by Fabrice Baudoin and published by Birkhäuser. This book was released on 2017-10-04 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Peacocks and Associated Martingales, with Explicit Constructions

Author : Francis Hirsch
Publisher : Springer Science & Business Media
ISBN 13 : 8847019087
Total Pages : 412 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Peacocks and Associated Martingales, with Explicit Constructions by : Francis Hirsch

Download or read book Peacocks and Associated Martingales, with Explicit Constructions written by Francis Hirsch and published by Springer Science & Business Media. This book was released on 2011-05-24 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings. They are developed in eight chapters, with about a hundred of exercises.

Long-Range Dependence and Self-Similarity

Author : Vladas Pipiras
Publisher : Cambridge University Press
ISBN 13 : 1108210198
Total Pages : 693 pages
Book Rating : 4.1/5 (82 download)

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Book Synopsis Long-Range Dependence and Self-Similarity by : Vladas Pipiras

Download or read book Long-Range Dependence and Self-Similarity written by Vladas Pipiras and published by Cambridge University Press. This book was released on 2017-04-18 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and self-similarity; central and non-central limit theorems for long-range dependent series, and the limiting Hermite processes; fractional Brownian motion and its stochastic calculus; several celebrated decompositions of fractional Brownian motion; multidimensional models for long-range dependence and self-similarity; and maximum likelihood estimation methods for long-range dependent time series. Designed for graduate students and researchers, each chapter of the book is supplemented by numerous exercises, some designed to test the reader's understanding, while others invite the reader to consider some of the open research problems in the field today.

Parameter Estimation in Stochastic Volatility Models

Author : Jaya P. N. Bishwal
Publisher : Springer Nature
ISBN 13 : 3031038614
Total Pages : 634 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Parameter Estimation in Stochastic Volatility Models by : Jaya P. N. Bishwal

Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Selected Aspects of Fractional Brownian Motion

Author : Ivan Nourdin
Publisher : Springer Science & Business Media
ISBN 13 : 884702823X
Total Pages : 133 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Selected Aspects of Fractional Brownian Motion by : Ivan Nourdin

Download or read book Selected Aspects of Fractional Brownian Motion written by Ivan Nourdin and published by Springer Science & Business Media. This book was released on 2013-01-17 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.

Real And Stochastic Analysis: Current Trends

Author : Malempati Madhusudana Rao
Publisher : World Scientific
ISBN 13 : 9814551295
Total Pages : 576 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Real And Stochastic Analysis: Current Trends by : Malempati Madhusudana Rao

Download or read book Real And Stochastic Analysis: Current Trends written by Malempati Madhusudana Rao and published by World Scientific. This book was released on 2013-11-26 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the current status and research trends in Stochastic Analysis. Several new and emerging research areas are described in detail, highlighting the present outlook in Stochastic Analysis and its impact on abstract analysis. The book focuses on treating problems in areas that serve as a launching pad for continual research.

Weak Convergence of Measures

Author : Vladimir I. Bogachev
Publisher : American Mathematical Soc.
ISBN 13 : 147044738X
Total Pages : 302 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Weak Convergence of Measures by : Vladimir I. Bogachev

Download or read book Weak Convergence of Measures written by Vladimir I. Bogachev and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.

Random Fields on the Sphere

Author : Domenico Marinucci
Publisher : Cambridge University Press
ISBN 13 : 1139499823
Total Pages : 354 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Random Fields on the Sphere by : Domenico Marinucci

Download or read book Random Fields on the Sphere written by Domenico Marinucci and published by Cambridge University Press. This book was released on 2011-08-25 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a comprehensive analysis of isotropic spherical random fields, with a view towards applications in cosmology. Any mathematician or statistician interested in these applications, especially the booming area of cosmic microwave background (CMB) radiation data analysis, will find the mathematical foundation they need in this book.

On the Estimation of Multiple Random Integrals and U-Statistics

Author : Péter Major
Publisher : Springer
ISBN 13 : 3642376177
Total Pages : 290 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis On the Estimation of Multiple Random Integrals and U-Statistics by : Péter Major

Download or read book On the Estimation of Multiple Random Integrals and U-Statistics written by Péter Major and published by Springer. This book was released on 2013-06-28 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work starts with the study of those limit theorems in probability theory for which classical methods do not work. In many cases some form of linearization can help to solve the problem, because the linearized version is simpler. But in order to apply such a method we have to show that the linearization causes a negligible error. The estimation of this error leads to some important large deviation type problems, and the main subject of this work is their investigation. We provide sharp estimates of the tail distribution of multiple integrals with respect to a normalized empirical measure and so-called degenerate U-statistics and also of the supremum of appropriate classes of such quantities. The proofs apply a number of useful techniques of modern probability that enable us to investigate the non-linear functionals of independent random variables. This lecture note yields insights into these methods, and may also be useful for those who only want some new tools to help them prove limit theorems when standard methods are not a viable option.

Stochastic Analysis for Poisson Point Processes

Author : Giovanni Peccati
Publisher : Springer
ISBN 13 : 3319052330
Total Pages : 359 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Stochastic Analysis for Poisson Point Processes by : Giovanni Peccati

Download or read book Stochastic Analysis for Poisson Point Processes written by Giovanni Peccati and published by Springer. This book was released on 2016-07-07 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.