Fractional Noise

Fractional Noise

A noise which is not completely independent of previous values. See Fractional Brownian Motion, 1/f Noise, White Noise.
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where [DELTA] is Laplacian, [[DELTA].sub.[alpha]] = -[(-[DELTA]).sup.[alpha]/2] is the fractional Laplacian generator on R, [[??].sup.H] is the fractional noise, and [??] is a (pure jump) Levy space-time white noise.
In Section 2, we briefly present some basic notations and preliminaries on the pseudo-differential operator [DELTA] + [[DELTA].sub.[alpha]], Levy space- time white noise, and fractional noise. In Section 3, we study the existence and uniqueness of the Walsh-mild solution to (1).
Fractional Noises. Let [B.sub.b](R) denote a class of bounded Borel sets in R and H [member of] (1/2, 1).
Wang, "On a stochastic heat equation with first order fractional noises and applications to finance," Journal of Mathematical Analysis and Applications, vol.
Zhou, "Stochastic generalized Burgers equations driven by fractional noises," Journal of Differential Equations, vol.
Yan, "On a semilinear stochastic partial differential equation with double-parameter fractional noises," Science China.
Van Ness, "Fractional Brownian motions, fractional noises and applications," SIAM Review, vol.
1968, Fractional Brownian motions, fractional noises and applications.
and Van Ness, J.: 1968, Fractional Brownian Motions, fractional noises, and applications.
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