Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4

By Mihai Gradinaru, Francesco Russo, Pierre Vallois. 2003

84 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/688321e7cac384926444f62585e976db8d878b0e

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Citations in the corpus

Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion (2007, methodology): “Instead of the pedestrian technique performed in [ 6 ] (as their authors called it themselves), we stress the fact that we chose here a more elegant way via Malliavin calculus.”
Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H∈(0,12) (2005, background): “1 of Gradinaru, Russo and Vallois [12], formula (5.”
Approximation at First and Second Order of $m$-order Integrals of the Fractional Brownian Motion and of Certain Semimartingales (2003, unknown): “1) (see [1], [3], [4], [7] and [8]).”
m-order integrals and generalized Ito's formula; the case of a fractional Brownian motion with any Hurst index (2005, methodology): “Also it is the sharp extension of the result of [15] obtained for H ≥ 1 4 .”
Stochastic integration with respect to Volterra processes (2003, methodology): “By a very different procedure, Gradinaru et al. [ GRV ] were able to include 1/4 in the domain of validity of the formula.”
Variations of the solution to a stochastic heat equation (2005, methodology): “One approach to studying these Riemann sums is through a regularization procedure developed by Russo, Vallois and coauthors [7, 8 , 14, 15].”
Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H=1/4 (2008, background): “By Theorem 3 in [16] (see also [2, 7, 8]), we have that ∫ 1”
Elements of Stochastic Calculus via Regularization (2006, background): “On this, the reader can consult [13, 27, 26].”
Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity (2018, background): “Gradinaru, Russo, and Vallois [18] extended this approach to p = 4 for functions of a fractional Brownian motion with Hurst index H ≥ 1/4, a result which relies heavily on the Gaussian properties of fractional Brownian motion.”