Are classes of deterministic integrands for fractional Brownian motion on an interval complete

By Vladas Pipiras, Murad S. Taqqu. 2001

161 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c74a7d7dc407204e9281942fcb1a1b0043bd3a40

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Citations in the corpus

Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions (2014, background): “The elements of the Hilbert space H, or more generally, of the space H⊗l may not be functions, but distributions; see [28] and [29].”
Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H∈(0,12) (2005, background): “In [25], Pipiras and Taqqu have shown that E (a,b] H is dense inλ (a,b] H .”
Fractional Brownian motion (2006, background): “It has been shown in [39] that the space |H | equipped with the inner product 〈·, ·〉H is not complete and it is isometric to a subspace of H .”
Representation formulae for the fractional Brownian motion (2009, methodology): “With this method, we obtain variables which are in the Gaussian space o f W, but we do not necessarily obtain the whole space, see the case of the fract ion l Brownian motion BH whenH > 1/2 in [34].”
A decomposition of the bifractional Brownian motion and some applications (2008, methodology): “In the case H > 1 2 , the space HBH contains distributions, according to the work by Pipiras and Taqqu [11].”
Variational solutions for partial differential equations driven by a fractional noise (2006, background): “…Wong-Zakäı approximations and related properties (see, for instance, [2], [3], [4], [6], [11], [15], [16], [17], [21], [26], [32], [44], [45], [52] and [53]), as well as to the proof of existence and uniqueness theorems for stochastic differential or integral equations as in [23],…”
Transformation formulas for fractional Brownian motion (2006, background): “For details on fractional Wiener integration over [0, T ] and R, see [12] and [13], respectively.”
On the Wiener integral with respect to the fractional Brownian motion on an interval (2007, background): “In the case H > 1/2 there are known some spaces of functions that are strict subsets of the domain of the integral because they are not complete (see Pipiras and Taqqu [6]).”
Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins (2008, methodology): “The constructions of the stochastic integral include restricting the integrand to specific classes of functions as in Dai and Heyde (1996), Gripenberg and Norros (1996), Lin (1995), Shiryaev (1998), using pathwise integration for the case of 1/2 H 1 as in Mikosch and Norvaisa (2000), applying Ma”