Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H∈(0,12)

By Patrick Cheridito, David Nualart. 2005

157 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/6651678e443525aa1818e0f8e0fa9a47eeae2ab7

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Citations in the corpus

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion (2008, methodology): “This approach was introduced by Decreusefond and ¨ Ust¨unel [5], and later developed by Carmona and Coutin [2], Duncan, Hu and Pasik-Duncan [7], Al`os, Mazet and Nualart [1], Hu and Oksendal [11], Cheridit o and Nualart [3], among others.”
Fractional stochastic differential equations with applications to finance (2013, methodology): “• The regularization approach was introduced by Russo and Vallois in [27, 28] and further developed by Cheridito and Nualart in [4].”
Variations of the solution to a stochastic heat equation (2005, methodology): “In fact, this result holds for any Hurst parameter H> 1/6, which was proven independently by Gradinaru, Nourdin, Russo and Vallois [7] and Cheridito and Nualart [ 2 ].”
Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter (2017, background): “For this reason, in Cheridito and Nualart (2005) the authors introduce an extended divergence integral δ∗ such that Dom δ∗ ∩ L2( ;H) = Dom δ and the extended divergence operator δ∗ restricted to Dom δ coincides with the divergence operator.”
Skorohod integration and stochastic calculus beyond the fractional Brownian scale (2005, methodology): “…to be uniquely defined, and to be useful: an Ito formula is established; it is employed to derive a Tanaka formula for a corresponding local time; linear additive and multiplicative stochastic differential equations are solved; an analysis of existence for the stochastic heat equation is given.”
ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL (2018, methodology): “In this case, the stochastic integration with respect to fBm should be interpreted as a divergence integral introduced by Cheridito and Nualart (2005). If we interpret the integral ∫ T 0 XtdXt in (2) as a Young integral, then, as T → ∞, κ̂LS = XT−X0 T ∫ T 0 Xtdt T − 1 2 X2 T−X 2 0 T 1 T ∫ T 0 X(2) t”
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”
Wiener integrals, Malliavin calculus and covariance measure structure (2006, unknown): “2H−|t−s|2H , t,s∈ [0,T]. (3) The process BH admits the Wiener integral representation (2) and the kernel Kand the space H can be characterized by the mean of fractional integrals and derivatives, see [2, 3, 10, 33, 7] among others. As a consequence, one can prove for any Hthe following Itˆo’s formul”
An Introduction to (Stochastic) Calculus with Respect to Fractional Brownian Motion (2007, methodology): “This work is done in [Dec03], [Dec05], or [ CN05 ].”