Turnpike Properties in the Calculus of Variations and Optimal Control, Alexander Zaslavski

Автор: Freguglia
Название: The Early Period of the Calculus of Variations
ISBN: 3319389440 ISBN-13(EAN): 9783319389448
Издательство: Springer
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Цена: 13275.00 р.
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Описание: This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders. Closely following the original papers and correspondences of Euler, Lagrange, the Bernoullis, and others, the reader is immersed in the challenge of theory building. We see what the founders were doing, the difficulties they faced, the mistakes they made, and their triumphs. The authors guide the reader through these works with instructive commentaries and complements to the original proofs, as well as offering a modern perspective where useful. The authors begin in 1697 with Johann Bernoulli’s work on the brachystochrone problem and the events leading up to it, marking the dawn of the calculus of variations. From there, they cover key advances in the theory up to the development of Lagrange’s ?-calculus, including: • The isoperimetrical problems• Shortest lines and geodesics• Euler’s Methodus Inveniendi and the two AdditamentaFinally, the authors give the readers a sense of how vast the calculus of variations has become in centuries hence, providing some idea of what lies outside the scope of the book as well as the current state of affairs in the field. This book will be of interest to anyone studying the calculus of variations who wants a deeper intuition for the techniques and ideas that are used, as well as historians of science and mathematics interested in the development and evolution of modern calculus and analysis.

Автор: Malliavin
Название: Stochastic Calculus of Variations in Mathematical Finance
ISBN: 3540434313 ISBN-13(EAN): 9783540434313
Издательство: Springer
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Цена: 12577.00 р.
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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.

Название: Calculus of Variations and Optimal Control Theory
ISBN: 0691151873 ISBN-13(EAN): 9780691151878
Издательство: Wiley
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Цена: 12672.00 р.
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Описание: Offers an introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. This book traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter.

Автор: Almeida Ricardo, Pooseh Shakoor, Torres Delfim F.
Название: Computational Methods in the Fractional Calculus of Variations
ISBN: 1783266406 ISBN-13(EAN): 9781783266401
Издательство: World Scientific Publishing
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Цена: 10296.00 р.
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Описание: This book fills a gap in the literature by introducing numerical techniques to solve problems of the Fractional Calculus of Variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.

Автор: Torres Delfim F. M.
Название: Introduction to the Fractional Calculus of Variations
ISBN: 1848169663 ISBN-13(EAN): 9781848169661
Издательство: World Scientific Publishing
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Цена: 10454.00 р.
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Описание: Suitable for graduate students and ambitious undergraduates in mathematics and mechanics, this title offers an introduction to the subject of Fractional Calculus of Variations (FCV). It describes non-conservative systems in mechanics.

Автор: Struwe Michael
Название: Plateau`s Problem and the Calculus of Variations. (MN-35):
ISBN: 0691607753 ISBN-13(EAN): 9780691607757
Издательство: Wiley
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Цена: 4752.00 р.
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Описание: This book is meant to give an account of recent developments in the theory of Plateau`s problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and re

Название: Introduction to the Calculus of Variations
ISBN: 1783265523 ISBN-13(EAN): 9781783265527
Издательство: World Scientific Publishing
Цена: 8870.00 р.
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Описание: The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving.