Описание: Malliavin calculus provides an infinite-dimensional differential calculus in the context of continuous paths stochastic processes. The calculus includes formulae of integration by parts and Sobolev spaces of differentiable functions defined on a probability space. This new book, demonstrating the relevance of Malliavin calculus for Mathematical Finance, starts with an exposition from scratch of this theory. Greeks (price sensitivities) are reinterpreted in terms of Malliavin calculus. Integration by parts formulae provide stable Monte Carlo schemes for numerical valuation of digital options. Finite-dimensional projections of infinite-dimensional Sobolev spaces lead to Monte Carlo computations of conditional expectations useful for computing American options. The discretization error of the Euler scheme for a stochastic differential equation is expressed as a generalized Watanabe distribution on the Wiener space. Insider information is expressed as an infinite-dimensional drift. The last chapter gives an introduction to the same objects in the context of jump processes where incomplete markets appear.
Описание: Portrays some of the important and innovative applications in stochastic control and finance, such as hedging in complete and incomplete markets, optimisation in the presence of asymmetric information and also pricing and sensitivity analysis. This book is suitable for graduate students, lecturers in stochastic analysis and applied researchers.
Описание: Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein–Uhlenbeck processes both with values in abstract Wiener spaces, L?vy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark–Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduate students, as well as to researchers interested in the techniques.
Автор: Malliavin Paul Название: Stochastic Analysis ISBN: 3540570241 ISBN-13(EAN): 9783540570240 Издательство: Springer Рейтинг: Цена: 9345 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book accounts in 5 independent parts, 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.
Автор: Berinde Vasile Название: Iterative Approximation of Fixed Points ISBN: 3540722335 ISBN-13(EAN): 9783540722335 Издательство: Springer Рейтинг: Цена: 5325 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The aim of this monograph is to give a unified introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. It summarizes the most significant contributions in the area by presenting, for each iterative method considered (Picard iteration, Krasnoselskij iteration, Mann iteration, Ishikawa iteration etc.), some of the most relevant, interesting, representative and actual convergence theorems. Applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods, are also presented. Due to the explosive number of research papers on the topic (in the last 15 years only, more than one thousand articles related to the subject were published), it was felt that such a monograph was imperatively necessary. The volume is useful for authors, editors, and reviewers. It introduces concrete criteria for evaluating and judging the plethora of published papers.
Автор: Chen Название: Normal Approximation by Stein`s Method ISBN: 3642150063 ISBN-13(EAN): 9783642150067 Издательство: Springer Рейтинг: Цена: 7012 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.
Описание: Although Normal Approximation and Asymptotic Expansions was first published in 1976, it has gained new significance and renewed interest among statisticians due to the developments of modern statistical techniques such as the bootstrap, the efficacy of which can be ascertained by asymptotic expansions. This is also the only book containing a detailed treatment of various refinements of the multivariate central limit theorem (CLT), including Berry–Essen-type error bounds for probabilities of general classes of functions and sets, and asymptotic expansions for both lattice and non-lattice distributions. With meticulous care, the authors develop the necessary background on: weak convergence theory, Fourier analysis, geometry of convex sets and the relationship between lattice random vectors and discrete subgroups of Rk.
Автор: Christensen Название: Approximation Theory ISBN: 0817636005 ISBN-13(EAN): 9780817636005 Издательство: Springer Рейтинг: Цена: 4674 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Gives an elementary introduction to approximation theory. This work demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. It is useful for students and instructors in pure and applied mathematics, mathematical physics, and engineering.
Автор: Holger Wendland Название: Scattered Data Approximation ISBN: 0521843359 ISBN-13(EAN): 9780521843355 Издательство: Cambridge Academ Рейтинг: Цена: 9574 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete
introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity.
The book starts with an
overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential
equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties,
numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading.
proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to support courses in computer aided geometric design, and
meshless methods for partial differential equations.
Автор: R. Wong Название: Asymptotic Approximation of Integrals ISBN: 0898714974 ISBN-13(EAN): 9780898714975 Издательство: Eurospan Рейтинг: Цена: 12079 р. Наличие на складе: Нет в наличии.
Описание: Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In this book, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, with references provided. Asymptotic Approximations of Integrals contains the ‘distributional method’, not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as ‘exponential asymptotics’. Expositions of these new theories are available in papers published in various journals, but not yet in book form.
Автор: Yann Bugeaud Название: Approximation by Algebraic Numbers ISBN: 0521045673 ISBN-13(EAN): 9780521045674 Издательство: Cambridge Academ Рейтинг: Цена: 6764 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Algebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed proofs. Starting from continued fractions and Khintchine’s theorem, Bugeaud introduces a variety of techniques, ranging from explicit constructions to metric number theory, including the theory of Hausdorff dimension. So armed, the reader is led to such celebrated advanced results as the proof of Mahler’s conjecture on S-numbers, the Jarnik–Besicovitch theorem, and the existence of T-numbers. Brief consideration is given both to the p-adic and the formal power series cases. Thus the book can be used for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the rich and comprehensive list of more than 600 references.
Описание: Approximation methods are vital in many challenging applications of computational science and engineering.This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing.It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems.An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales.Contributions of industrial mathematicians, including representatives from Microsoft and Schlumberger, foster the transfer of the latest approximation methods to real-world applications.
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