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| Author | : Laurent Decreusefond |
| Publisher | : Springer Nature |
| Total Pages | : 180 |
| Release | : 2022-06-23 |
| Genre | : Mathematics |
| ISBN | : 3031013115 |
Download Selected Topics in Malliavin Calculus Book in PDF, ePub and Kindle
This book is not a research monograph about Malliavin calculus with the latest results and the most sophisticated proofs. It does not contain all the results which are known even for the basic subjects which are addressed here. The goal was to give the largest possible variety of proof techniques. For instance, we did not focus on the proof of concentration inequality for functionals of the Brownian motion, as it closely follows the lines of the analog result for Poisson functionals. This book grew from the graduate courses I gave at Paris-Sorbonne and Paris-Saclay universities, during the last few years. It is supposed to be as accessible as possible for students who have knowledge of Itô calculus and some rudiments of functional analysis.
| Author | : |
| Publisher | : |
| Total Pages | : 266 |
| Release | : 1995 |
| Genre | : Malliavin calculus |
| ISBN | : 9781475724394 |
Download The Malliavin Calculus and Related Topics Book in PDF, ePub and Kindle
Readers are assumed to have a firm grounding in probability as might be gained from a graduate course in the subject. Exercises at the end of each chapter help to reinforce a reader's understanding and to extend some of the ideas covered, and each chapter ends with a discussion of further directions that research has taken.
| Author | : David Nualart |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 273 |
| Release | : 2013-12-11 |
| Genre | : Mathematics |
| ISBN | : 1475724373 |
Download The Malliavin Calculus and Related Topics Book in PDF, ePub and Kindle
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 | : David Nualart |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 99 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 0821847791 |
Download Malliavin Calculus and Its Applications Book in PDF, ePub and Kindle
The Malliavin calculus was developed to provide a probabilistic proof of Hormander's hypoellipticity theorem. The theory has expanded to encompass other significant applications. The main application of the Malliavin calculus is to establish the regularity of the probability distribution of functionals of an underlying Gaussian process. In this way, one can prove the existence and smoothness of the density for solutions of various stochastic differential equations. More recently, applications of the Malliavin calculus in areas such as stochastic calculus for fractional Brownian motion, central limit theorems for multiple stochastic integrals, and mathematical finance have emerged. The first part of the book covers the basic results of the Malliavin calculus. The middle part establishes the existence and smoothness results that then lead to the proof of Hormander's hypoellipticity theorem. The last part discusses the recent developments for Brownian motion, central limit theorems, and mathematical finance.
| Author | : Christos H Skiadas |
| Publisher | : World Scientific |
| Total Pages | : 436 |
| Release | : 2009-05-13 |
| Genre | : Technology & Engineering |
| ISBN | : 9814468231 |
Download Topics On Chaotic Systems: Selected Papers From Chaos 2008 International Conference Book in PDF, ePub and Kindle
This volume includes the best papers presented at the CHAOS 2008 International Conference on Chaotic Modeling, Simulation and Applications. It provides a valuable collection of new ideas, methods, and techniques in the field of nonlinear dynamics, chaos, fractals and their applications in general science and in engineering sciences.It touches on many fields such as chaos, dynamical systems, nonlinear systems, fractals and chaotic attractors. It also covers mechanics, hydrofluid dynamics, chaos in meteorology and cosmology, Hamiltonian and quantum chaos, chaos in biology and genetics, chaotic control, and chaos in economy and markets, and chaotic simulations; thus, containing cutting-edge interdisciplinary research with high-interest applications.These contributions present new solutions by analyzing the relevant data and through the use of recent advances in different fields, especially in chaotic simulation methods and techniques.
| Author | : Ivan Nourdin |
| Publisher | : Cambridge University Press |
| Total Pages | : 255 |
| Release | : 2012-05-10 |
| Genre | : Mathematics |
| ISBN | : 1107017777 |
Download Normal Approximations with Malliavin Calculus Book in PDF, ePub and Kindle
This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
| Author | : Giuseppe Da Prato |
| Publisher | : Springer |
| Total Pages | : 279 |
| Release | : 2014-07-01 |
| Genre | : Mathematics |
| ISBN | : 8876424997 |
Download Introduction to Stochastic Analysis and Malliavin Calculus Book in PDF, ePub and Kindle
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 | : Vladimir Igorevich Bogachev |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 506 |
| Release | : 2010-07-21 |
| Genre | : Mathematics |
| ISBN | : 082184993X |
Download Differentiable Measures and the Malliavin Calculus Book in PDF, ePub and Kindle
This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.
| Author | : Marta Sanz-Sole |
| Publisher | : CRC Press |
| Total Pages | : 172 |
| Release | : 2005-08-17 |
| Genre | : Mathematics |
| ISBN | : 1439818940 |
Download Malliavin Calculus with Applications to Stochastic Partial Differential Equations Book in PDF, ePub and Kindle
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 present
| Author | : Palle Jorgensen |
| Publisher | : World Scientific |
| Total Pages | : 253 |
| Release | : 2021-01-15 |
| Genre | : Mathematics |
| ISBN | : 9811225796 |
Download Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory Book in PDF, ePub and Kindle
The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.
