Loeb measures in practice : recent advances / Nigel J. Cutland
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1751Langue : anglais.Éditeur : Berlin : Springer, 2000ISBN: 9783540413844.ISSN: 1617-9692.Sujet MSC : 28E05, Miscellaneous topics in measure theory, Nonstandard measure theory03H05, Mathematical logic and foundations, Nonstandard models in mathematics
76D05, Fluid mechanics, Navier-Stokes equations for incompressible viscous fluids
60H07, Probability theory and stochastic processes - Stochastic analysis, Stochastic calculus of variations and the Malliavin calculus
60H30, Probability theory and stochastic processes - Stochastic analysis, Applications of stochastic analysis (to PDEs, etc.)En-ligne : Springerlink | Zentralblatt | MathSciNet
... Chapter 1, entitled “Loeb measures,” contains a very readable and attractive account of the methods of nonstandard analysis that play an important role in the applications to follow. Stochastic fluid mechanics is the topic of Chapter 2. It is the longest of the monograph and deals with various aspects of the theory of the Navier-Stokes equations. The so-called flat integral representation of the Wiener measure and Brownian motion along with the Malliavin calculus are treated in Chapter 3. The Black-Scholes method is the main topic of the last Chapter 4 and highlights certain aspects of the mathematical finance theory. The author is to be commended for the brilliant manner in which he has been able to present such a convincing treatment of these important topics based in the nonstandard theory of measures and their constructions in about 100 pages. (Zentralblatt)
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