Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Generalized Functionals of Brownian Motion and Their Applications: Nonlinear Functionals of Fundamental Stochastic Processes

Generalized Functionals of Brownian Motion and Their Applications: Nonlinear Functionals of Fundamental Stochastic Processes

Ahmed, N. U.

Hardcover

General MathematicsProbability & Statistics

ISBN10: 9814366366
ISBN13: 9789814366366
Publisher: World Scientific Publishing Company
Published: Oct 3 2011
Pages: 316
Weight: 1.35
Height: 0.90 Width: 6.10 Depth: 9.00
Language: English
This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process -- covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems.Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz-Fischer theorem for separable Hilbert spaces and the space of Wiener-Ito functionals is drawn out, thus providing a clear insight into the subject.

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