Integration questions related to fractional Brownian motion

By Vladas Pipiras, Murad S. Taqqu. 2000

424 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a3354b63f5f63fb1be3fe152098280e611ea40c0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Mathematical Physics

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].”
A version of Hörmander’s theorem for the fractional Brownian motion (2007, background): “It can be shown that L 1/H ([0,1],R d ) ⊂ H but that H also contains distributions (see for example [ 21 ]).”
Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4 (2003, methodology): “Other recent papers where similar techniques have been used are for instance by [23] and [32].”
An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter (2003, neutral): “By Lemma 3.1 in Pipiras and Taqqu (2000) (t − s)H−1=2+ − (−s)H−1=2+ = (H + 1=2)(D−(H−1=2)− 1(0; t))(s) holds.”
NO ARBITRAGE UNDER TRANSACTION COSTS, WITH FRACTIONAL BROWNIAN MOTION AND BEYOND (2006, background): “In fact, Rogers (1997), Salopek (1998), Shiryaev (1998), Dasgupta & Kallianpur (2000) and Cheridito (2003) have shown that it allows outright arbitrage in a number of ways.”
Stochastic Processes Induced by Singular Operators (2011, background): “The set of functions ψ such that q σ (ψ) 29 , Theorem 3.”
Out of sample forecasts of quadratic variation (2008, neutral): “f(u)g(v) |u − v| 2H−2 dv du (3.18) (see Pipiras and Taqqu (2000) ).”
Fractional Ornstein-Uhlenbeck processes (2003, background): “For all H ∈ (0, 1), the functions f(x) = 1{x≤0}eλx and g(x) = 1{x≤s}e λx belong to the inner product space Λ̃H defined on page 289 of Pipiras and Taqqu (2000).”
Stochastic heat equation driven by fractional noise and local time (2007, background): “In this case the space H is not a space of functions (see [14]) because it contains distributions.”
Variational solutions for partial differential equations driven by a fractional noise (2006, background): “…inequalities, 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…”
Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H (2006, methodology): “Hence it is convenient to introduce the Banach space jHj of measurable functions j on [0, T ] satisfying kjk 2 jHj :¼ AE ð T 0 ð T 0 jj(r)j jj(u)j jr À uj 2 HÀ2 dr du , 1: One can prove (Pipiras and Taqqu 2000) that the space jHj equipped with the inner product hj, łi H is not complete.”
Wiener Integrals with Respect to the Hermite Process and a Non-Central Limit Theorem (2007, background): “The followings facts has also been proved in [ 18 ]:”