Change Of Time And Change Of Measure, Barndorff-Nielsen Ole E Et Al
Автор: Barndorff-Nielsen Ole E Et Al Название: Change Of Time And Change Of Measure (Second Edition) ISBN: 9814678589 ISBN-13(EAN): 9789814678582 Издательство: World Scientific Publishing Рейтинг: Цена: 8870.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.
Описание: Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach features an introduction to the mathematical theory underlying the financial models that were developed and employed on Wall Street.
Measure Theory and Fine Properties of Functions, Revised Edition provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.
Topics covered include a quick review of abstract measure theory, theorems and differentiation in ℝn, Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions as well as functions of bounded variation.
The text provides complete proofs of many key results omitted from other books, including Besicovitch's covering theorem, Rademacher's theorem (on the differentiability a.e. of Lipschitz functions), area and coarea formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Aleksandrov's theorem (on the twice differentiability a.e. of convex functions).
This revised edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the π-λ theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated.
Topics are carefully selected and the proofs are succinct, but complete. This book provides ideal reading for mathematicians and graduate students in pure and applied mathematics.
Автор: Wheeden Название: Measure and Integral ISBN: 1498702899 ISBN-13(EAN): 9781498702898 Издательство: Taylor&Francis Рейтинг: Цена: 17609.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content.
Published nearly forty years after the first edition, this long-awaited Second Edition also:
Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 p
Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case
Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of Hцlder continuous functions and the space of functions of bounded mean oscillation
Derives a subrepresentation formula, which in higher dimensions plays a role roughly similar to the one played by the fundamental theorem of calculus in one dimension
Extends the subrepresentation formula derived for smooth functions to functions with a weak gradient
Applies the norm estimates derived for fractional integral operators to obtain local and global first-order Poincarй-Sobolev inequalities, including endpoint cases
Proves the existence of a tangent plane to the graph of a Lipschitz function of several variables
Includes many new exercises not present in the first edition
This widely used and highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians.
Автор: Capinski Название: Measure, Integral and Probability ISBN: 1852337818 ISBN-13(EAN): 9781852337810 Издательство: Springer Рейтинг: Цена: 4884.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: В· a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales В· key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.
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