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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Generalized Functionals Of Brownian Motion And Their Applications: Nonlinear Functionals Of Fundamental Stochastic Processes (Hardcover)
Loot Price: R1,994
Discovery Miles 19 940
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Generalized Functionals Of Brownian Motion And Their Applications: Nonlinear Functionals Of Fundamental Stochastic Processes (Hardcover)
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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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