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The Malliavin Calculus and Related Topics

The Malliavin Calculus and Related Topics Author David Nualart
ISBN-10 9783540283294
Release 2006-02-27
Pages 382
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The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hörmander's sum of squares theorem but has found a range of applications in stochastic analysis. This book presents the features of Malliavin calculus and discusses its main applications. This second edition includes recent applications in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.



The Malliavin Calculus and Related Topics

The Malliavin Calculus and Related Topics Author David Nualart
ISBN-10 9781475724370
Release 2013-12-11
Pages 266
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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.



The Malliavin Calculus

The Malliavin Calculus Author Denis R. Bell
ISBN-10 9780486152059
Release 2012-12-03
Pages 128
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This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.



Malliavin Calculus for L vy Processes with Applications to Finance

Malliavin Calculus for L  vy Processes with Applications to Finance Author Giulia Di Nunno
ISBN-10 3540785728
Release 2008-10-08
Pages 418
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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.



Integration and Probability

Integration and Probability Author Paul Malliavin
ISBN-10 9781461242024
Release 2012-12-06
Pages 326
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An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution gives a taste of the fact that analysis is not a collection of independent theories, but can be treated as a whole.



Stochastic Partial Differential Equations

Stochastic Partial Differential Equations Author Helge Holden
ISBN-10 9780387894881
Release 2009-12-01
Pages 305
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The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Lévy process noise. Applications of the theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter.



Probability in Banach Spaces

Probability in Banach Spaces Author Michel Ledoux
ISBN-10 9783642202124
Release 2013-03-09
Pages 480
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Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.



Stochastic Calculus of Variations in Mathematical Finance

Stochastic Calculus of Variations in Mathematical Finance Author Paul Malliavin
ISBN-10 9783540307990
Release 2006-02-25
Pages 142
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Highly esteemed author Topics covered are relevant and timely



Introduction to Malliavin Calculus

Introduction to Malliavin Calculus Author David Nualart
ISBN-10 1107611989
Release 2018-09-30
Pages 246
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This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lévy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.



Diffusions and Elliptic Operators

Diffusions and Elliptic Operators Author Richard F. Bass
ISBN-10 9780387226040
Release 2006-05-11
Pages 232
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A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE, and moves on to probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions. The author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators, as well as Martingale problems and the Malliavin calculus. While serving as a textbook for a graduate course on diffusion theory with applications to PDE, this will also be a valuable reference to researchers in probability who are interested in PDE, as well as for analysts interested in probabilistic methods.



Generalized Functionals of Brownian Motion and Their Applications

Generalized Functionals of Brownian Motion and Their Applications Author Nasir Uddin Ahmed
ISBN-10 9789814366373
Release 2012
Pages 299
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This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process OCo covering the classical WienerOCoIto class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the WienerOCoSobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems. Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated RieszOCoFischer theorem for separable Hilbert spaces and the space of WienerOCoIto functionals is drawn out, thus providing a clear insight into the subject.



Malliavin Calculus for L vy Processes with Applications to Finance

Malliavin Calculus for L  vy Processes with Applications to Finance Author Giulia Di Nunno
ISBN-10 3540785728
Release 2008-10-08
Pages 418
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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.



Stochastic Calculus and Applications

Stochastic Calculus and Applications Author Samuel Cohen
ISBN-10 9781493928675
Release 2015-11-18
Pages 666
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Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition)



Malliavin Calculus with Applications to Stochastic Partial Differential Equations

Malliavin Calculus with Applications to Stochastic Partial Differential Equations Author Marta Sanz-Sole
ISBN-10 1439818940
Release 2005-08-17
Pages 150
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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.



The Malliavin Calculus

The Malliavin Calculus Author Denis R. Bell
ISBN-10 9780486152059
Release 2012-12-03
Pages 128
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This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.



Stochastic Processes Finance and Control

Stochastic Processes  Finance and Control Author Robert J. Elliot
ISBN-10 9789814383301
Release 2012
Pages 588
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This Festschrift is dedicated to Robert J Elliott on the occasion of his 70th birthday It brings together a collection of chapters by distinguished and eminent scholars in the fields of stochastic processes, filtering and control, as well as their applications to mathematical finance It presents cutting edge developments in these fields and is a valuable source of references for researchers, graduate students and market practitioners in mathematical finance and financial engineering Topics include the theory of stochastic processes, differential and stochastic games, mathematical finance, filtering and control.



Normal Approximations with Malliavin Calculus

Normal Approximations with Malliavin Calculus Author Ivan Nourdin
ISBN-10 9781107017771
Release 2012-05-10
Pages 239
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