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Author Index, Small Hurst ♦ Unterberger, Jérémie
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Multidimensional Fractional Brownian Motion ♦ Vy Area ♦ Stochastic Calculus ♦ Small Lder Regularity Index ♦ Rough Path Theory ♦ Iterated Integral ♦ Stochastic Differential Equation ♦ Multidimensional Process ♦ Short Note ♦ Main Tool ♦ Particular Case ♦ Main Idea ♦ Explicit Construction ♦ Fourier Normal Ordering ♦ Rough Path ♦ Arbitrary Hurst Index ♦ Fractional Brownian Motion ♦ Abstract Argument ♦ Standard Argument
Abstract The main tool for stochastic calculus with respect to a multidimensional process B with small Hölder regularity index is rough path theory. Once B has been lifted to a rough path, a stochastic calculus – as well as solutions to stochastic differential equations driven by B – follow by standard arguments. Although such a lift has been proved to exist by abstract arguments [19], a first general, explicit construction has been proposed in [27, 28] under the name of Fourier normal ordering. The purpose of this short note is to convey the main ideas of the Fourier normal ordering method in the particular case of the iterated integrals of lowest order of fractional Brownian motion with arbitrary Hurst index.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Publisher Date 2009-01-01