A General Fractional White Noise Theory And Applications To Finance

By Robert J. R. Elliott, John van der Hoek. 2003

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On the characteristics of a class of Gaussian processes within the white noise space setting (2009, methodology): “…rewritten as a double integral as explained in the previous section: the operator T m reduces, up to a multiplicative constant, to the operator M H deﬁned in [19, (2.10) and using [20, Formula 12, p. 170], that is, in the sense of distributions, The operator T m will play a key role in the sequel.”
Arbitrage with fractional Brownian motion (2007, methodology): “We now recall the notion of a Wick-self-financing portfolio from [12] (cf.”
MULTIFRACTIONAL STOCHASTIC VOLATILITY MODELS (2011, unknown): “Various approaches have been developed since, based mainly on Malliavin calculus [25, 2], pathwise integrals [65], rough paths [24], and white noise theory [31, 12, 10].”
Stochastic Calculus with Respect to Gaussian Processes (2014, background): “The reader interested in an exhaustive overview of the subject may refer to [10, 37, 43] for divergence type integral and to [4, 7, 11, 42] for integral in the white noise theory framework.”
Fractional Brownian motion (2006, methodology): “Applying the stochastic calculus with respect to the Wick integral, Hu and Øksendal in [22], and Elliott and Hoek in [16] have derived the following formula for the value”