The Malliavin CalculusCourier Corporation, 3 de dez. de 2012 - 128 páginas This introduction to Malliavin's stochastic calculus of variations is suitable for graduate students and professional mathematicians. Author Denis R. Bell particularly emphasizes the problem that motivated the subject's development, with detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and descriptions of a variety of applications. The first chapter covers enough technical background to make the subsequent material accessible to readers without specialized knowledge of stochastic analysis. Succeeding chapters examine the functional analytic and variational approaches (with extensive explorations of the work of Stroock and Bismut); and elementary derivation of Malliavin's inequalities and a discussion of the different forms of the theory; and the non-degeneracy of the covariance matrix under Hormander's condition. The text concludes with a brief survey of applications of the Malliavin calculus to problems other than Hormander's. |
Conteúdo
The functional analytic approach | 16 |
The variational approach | 34 |
An elementary derivation of Malliavins inequalities | 46 |
Nondegeneracy of the covariance matrix under Hörmanders | 73 |
Some further applications of the Malliavin calculus | 87 |
| 103 | |
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Termos e frases comuns
absolutely continuous abstract Wiener space argument Banach space Borel measure Brownian motion C(RP chapter continuous with respect converges defined denote differentiable with respect domain dy(w dy(x exists a constant finite following result follows from Lemma Furthermore Gaussian measure Girsanov theorem gives GL(d Hence Hilbert space Hilbert–Schmidt Hörmander's condition Hörmander's theorem implies independent inequality infinite dimensional inner product invertible iterating Itô's lemma kt/m L*-norm Lebesgue measure Lipschitz Malliavin calculus map g measures induced n-dimensional Brownian motion non-negative norm Note obtained orthonormal basis path polynomial proof of Theorem prove quasi-invariant random variable real-valued satisfies the equation sequence shown ſº solution stochastic differential equation stochastic integral Stratonovich Stroock and Bismut subspace Suppose teſ test function Theorem 1.9(iv Theorem 2.5 vector fields Wiener measure