Malliavin Calculus And Stochastic Analysis

Author : Frederi Viens,Jin Feng,Yaozhong Hu,Eulalia Nualart
Publisher : Springer Science & Business Media
Page : 580 pages
File Size : 50,5 Mb
Release : 2013-02-15
Category : Mathematics
ISBN : 9781461459064

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Malliavin Calculus and Stochastic Analysis by Frederi Viens,Jin Feng,Yaozhong Hu,Eulalia Nualart Pdf

The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline. Stochastic analysis provides a fruitful interpretation of this calculus, particularly as described by David Nualart and the scores of mathematicians he influences and with whom he collaborates. Many of these, including leading stochastic analysts and junior researchers, presented their cutting-edge research at an international conference in honor of David Nualart's career, on March 19-21, 2011, at the University of Kansas, USA. These scholars and other top-level mathematicians have kindly contributed research articles for this refereed volume.

Author : Giovanni Peccati,Matthias Reitzner
Publisher : Springer
Page : 346 pages
File Size : 50,6 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.

Author : Giuseppe Da Prato
Publisher : Springer
Page : 279 pages
File Size : 43,8 Mb
Release : 2014-07-01
Category : Mathematics
ISBN : 9788876424991

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Introduction to Stochastic Analysis and Malliavin Calculus by Giuseppe Da Prato Pdf

This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Itô's formula. The second part deals with differential stochastic equations and their connection with parabolic problems. The third part provides an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems. In this third edition several small improvements are added and a new section devoted to the differentiability of the Feynman-Kac semigroup is introduced. A considerable number of corrections and improvements have been made.

Author : Paul Malliavin
Publisher : Springer
Page : 346 pages
File Size : 49,5 Mb
Release : 2015-06-12
Category : Mathematics
ISBN : 9783642150746

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Stochastic Analysis by Paul Malliavin Pdf

In 5 independent sections, this book accounts recent main developments of stochastic analysis: Gross-Stroock Sobolev space over a Gaussian probability space; quasi-sure analysis; anticipate stochastic integrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension.

Author : Hiroyuki Matsumoto,Setsuo Taniguchi
Publisher : Cambridge University Press
Page : 359 pages
File Size : 47,6 Mb
Release : 2017
Category : Mathematics
ISBN : 9781107140516

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Stochastic Analysis by Hiroyuki Matsumoto,Setsuo Taniguchi Pdf

Developing the Itô calculus and Malliavin calculus in tandem, this book crystallizes modern day stochastic analysis into a single volume.

Author : David Nualart
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 54,9 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781475724370

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The Malliavin Calculus and Related Topics by David Nualart Pdf

The origin of this book lies in an invitation to give a series of lectures on Malliavin calculus at the Probability Seminar of Venezuela, in April 1985. The contents of these lectures were published in Spanish in [176]. Later these notes were completed and improved in two courses on Malliavin cal culus given at the University of California at Irvine in 1986 and at Ecole Polytechnique Federale de Lausanne in 1989. The contents of these courses correspond to the material presented in Chapters 1 and 2 of this book. Chapter 3 deals with the anticipating stochastic calculus and it was de veloped from our collaboration with Moshe Zakai and Etienne Pardoux. The series of lectures given at the Eighth Chilean Winter School in Prob ability and Statistics, at Santiago de Chile, in July 1989, allowed us to write a pedagogical approach to the anticipating calculus which is the basis of Chapter 3. Chapter 4 deals with the nonlinear transformations of the Wiener measure and their applications to the study of the Markov property for solutions to stochastic differential equations with boundary conditions.

Author : Giulia Di Nunno,Bernt Øksendal,Frank Proske
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 55,8 Mb
Release : 2008-10-08
Category : Mathematics
ISBN : 9783540785729

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Malliavin Calculus for Lévy Processes with Applications to Finance by Giulia Di Nunno,Bernt Øksendal,Frank Proske Pdf

This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.

Author : Springer
Publisher : Unknown
Page : 596 pages
File Size : 48,8 Mb
Release : 2013-02-01
Category : Electronic
ISBN : 1461459079

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Malliavin Calculus and Stochastic Analysis by Springer Pdf

Author : Marta Sanz-Sole
Publisher : CRC Press
Page : 150 pages
File Size : 46,5 Mb
Release : 2005-08-17
Category : Mathematics
ISBN : 1439818940

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Malliavin Calculus with Applications to Stochastic Partial Differential Equations by Marta Sanz-Sole Pdf

Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics. This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself based on a general Gaussian space, going from the simple, finite-dimensional setting to the infinite-dimensional one. The final three chapters discuss recent research on regularity of the solution of stochastic partial differential equations and the existence and smoothness of their probability laws. About the author: Marta Sanz-Solé is Professor at the Faculty of Mathematics, University of Barcelona. She is a leading member of the research group on stochastic analysis at Barcelona, and in 1998 she received the Narcis Monturiol Award of Scientific and Technological Excellence from the autonomous government of Catalonia.

Author : David Nualart,Eulalia Nualart
Publisher : Cambridge University Press
Page : 249 pages
File Size : 48,7 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781107039124

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Introduction to Malliavin Calculus by David Nualart,Eulalia Nualart Pdf

A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

Author : H. Körezlioglu,A.S. Üstünel
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203735

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Stochastic Analysis and Related Topics by H. Körezlioglu,A.S. Üstünel Pdf

This volume contains a large spectrum of work: super processes, Dirichlet forms, anticipative stochastic calculus, random fields and Wiener space analysis. The first part of the volume consists of two main lectures given at the third Silivri meeting in 1990: 1. "Infinitely divisible random measures and superprocesses" by D.A. Dawson, 2. "Dirichlet forms on infinite dimensional spaces and appli cations" by M. Rockner. The second part consists of recent research papers all related to Stochastic Analysis, motivated by stochastic partial differ ential equations, Markov fields, the Malliavin calculus and the Feynman path integrals. We would herewith like to thank the ENST for its material support for the above mentioned meeting as well as for the ini tial preparation of this volume and to our friend and colleague Erhan Qmlar whose help and encouragement for the realization of this volume have been essential. H. Korezlioglu A.S. Ustiinel INFINITELY DIVISIBLE RANDOM MEASURES AND SUPERPROCESSES DONALD A. DAWSON 1. Introduction.

Author : Ciprian Tudor
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 51,5 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.

Author : Paul Malliavin,Anton Thalmaier
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 50,7 Mb
Release : 2006-02-25
Category : Business & Economics
ISBN : 9783540307990

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Stochastic Calculus of Variations in Mathematical Finance by Paul Malliavin,Anton Thalmaier Pdf

Highly esteemed author Topics covered are relevant and timely

Author : Elisa Alos,David Garcia Lorite
Publisher : CRC Press
Page : 350 pages
File Size : 44,9 Mb
Release : 2021-07-14
Category : Mathematics
ISBN : 9781000403510

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Malliavin Calculus in Finance by Elisa Alos,David Garcia Lorite Pdf

Malliavin Calculus in Finance: Theory and Practice aims to introduce the study of stochastic volatility (SV) models via Malliavin Calculus. Malliavin calculus has had a profound impact on stochastic analysis. Originally motivated by the study of the existence of smooth densities of certain random variables, it has proved to be a useful tool in many other problems. In particular, it has found applications in quantitative finance, as in the computation of hedging strategies or the efficient estimation of the Greeks. The objective of this book is to offer a bridge between theory and practice. It shows that Malliavin calculus is an easy-to-apply tool that allows us to recover, unify, and generalize several previous results in the literature on stochastic volatility modeling related to the vanilla, the forward, and the VIX implied volatility surfaces. It can be applied to local, stochastic, and also to rough volatilities (driven by a fractional Brownian motion) leading to simple and explicit results. Features Intermediate-advanced level text on quantitative finance, oriented to practitioners with a basic background in stochastic analysis, which could also be useful for researchers and students in quantitative finance Includes examples on concrete models such as the Heston, the SABR and rough volatilities, as well as several numerical experiments and the corresponding Python scripts Covers applications on vanillas, forward start options, and options on the VIX. The book also has a Github repository with the Python library corresponding to the numerical examples in the text. The library has been implemented so that the users can re-use the numerical code for building their examples. The repository can be accessed here: https://bit.ly/2KNex2Y.

Author : Nicolas Privault
Publisher : Springer
Page : 282 pages
File Size : 40,8 Mb
Release : 2009-07-14
Category : Mathematics
ISBN : 9783642023804

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Stochastic Analysis in Discrete and Continuous Settings by Nicolas Privault Pdf

This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.