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- W2029239285 abstract "Maruyama introduced the notation d b ( t ) = w ( t ) ( d t ) 1 / 2 where w ( t ) is a zero-mean Gaussian white noise, in order to represent the Brownian motion b ( t ) . Here, we examine in which way this notation can be extended to Brownian motion of fractional order a (different from 1/2) defined as the Riemann–Liouville derivative of the Gaussian white noise. The rationale is mainly based upon the Taylor’s series of fractional order, and two cases have to be considered: processes with short-range dependence, that is to say with 0 ⊲ a ≤ 1 / 2 , and processes with long-range dependence, with 1 / 2 ⊲ a ≤ 1 ." @default.
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- W2029239285 date "2005-07-01" @default.
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- W2029239285 title "On the representation of fractional Brownian motion as an integral with respect to <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mstyle mathvariant=normal><mml:mi>d</mml:mi></mml:mstyle><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:msup></mml:math>" @default.
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- W2029239285 doi "https://doi.org/10.1016/j.aml.2004.05.014" @default.
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