Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 12

By Elisa Alòs, O. Mazet, David Nualart. 2000

67 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/113d309bddede4ee1dc72231862661578540aaa7

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Citations in the corpus

Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4 (2003, background): “Ustunel [11] and it was studied intensively, see [6], [1] and [2], even when the integrator is a more general Gaussian process.”
STOCHASTIC STRATONOVICH CALCULUS fBm FOR FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER LESS THAN 1/2 (2001, background): “The forward integral with respect to the fractional Brownian motion of index H < 1/2 has been studied in [1].”
STOCHASTIC INTEGRATION FOR FRACTIONAL BROWNIAN MOTION IN A HILBERT SPACE (2006, unknown): “The stochastic calculus given here uses a different approach than the one used in [1], [3] or [4].”
Stochastic Calculus with Respect to Gaussian Processes (2001, background): “In the case of the fractional Brownian motion with parameter H < 2 the class of integrable processes (in the Stratonovich sense) has been characterized in [2] using classical fractional calculus.”
An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter (2003, methodology): “Following this approach all Hurst parameters can be considered (see AlKos and Nualart (2000) for H ¿ 12 , AlKos et al. (2000) for H ¡ 1 2 and more generally AlKos et al. (2001) for Gaussian processes with suitable properties).”
Dynamic models of long-memory processes driven by Lévy noise (2002, background): “One approach is to develop a theory of stochastic differential equations driven by fractional Brownian motion (FBM), which is a classical example of a nonstationary Gaussian process with LRD (see [2], [22], [23], [25], [39], [48]).”
HURST EXPONENT ESTIMATION OF LOCALLY SELF-SIMILAR GAUSSIAN PROCESSES USING SAMPLE QUANTILES (2005, methodology): “Alòs et al. (1999) which is an H-self-similar centered Gaussian process but with increments satisfying only some kind of local stationarity, see Remark 2 for more details. Let us be more specific on the construction of the wavelet decomposition method, see e.g. Flandrin (1992): the authors noticed t”
Fractional Backward Stochastic Differential Equations and Fractional Backward Variational Inequalities (2011, background): “[1] for H < 1/2 as well as in Alòs et al.”
Approximation at First and Second Order of $m$-order Integrals of the Fractional Brownian Motion and of Certain Semimartingales (2003, background): “Let us recall (see, for instance, [1], p. 122) that the fractional Brownian motion can be written as where, here and elsewhere we denote by (cid:176) H the constant ¡( H + ) ¡ 1 .”
Fractional Brownian motion (2006, methodology): “The 1/H -variation of Wick stochastic integrals with respect to the fractional Brownian motion with parameter H > 1/2 has been computed by Guerra and Nualart in [20].”