Stochastic Calculus with Respect to Gaussian Processes

By E. Alòs, O. Mazet, David Nualart. 2001

309 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/e6333dd84a65d924821ffbc714eaab4fa0470814

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Citations in the corpus

Variational solutions for partial differential equations driven by a fractional noise (2006, background): “formulae, maximal 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 equation”
Skorohod integration and stochastic calculus beyond the fractional Brownian scale (2005, methodology): “To guarantee that is increasing, we can again invoke the flexibility on the choice of h, combined with the fact that = o(1).”
An S-transform approach to integration with respect to a fractional Brownian motion (2003, methodology): “For this reason the Malliavin calculus approach in Al6s et al. (2001) is only developed for H > .”
MULTIFRACTIONAL STOCHASTIC VOLATILITY MODELS (2011, unknown): “As far as mBm is concerned, we note first that the Skohorod integral developed for instance in [2] does not seem to be easily adaptable to mBm, as it would require writing B as a Wiener integral over a finite interval.”
Distribution dependent SDEs driven by fractional Brownian motions (2021, background): “Consequently, by [2] again, the process {Wt = B ((K H) −1 I[0,t]), t ∈ [0, T ]} is a Wiener process, and B has the following Volterra-type representation B t = ∫ t”
Fractional stochastic differential equations with applications to finance (2013, methodology): “• The Malliavin calculus approach was introduced by Decreusefond and Üstünel in [7] for fBm and extended to more general Gaussian processes by Alos, Mazet, and Nualart in [1], Decreusefond in [8], etc.”
Stein estimation for the drift of Gaussian processes using the Malliavin calculus (2008, unknown): “s)h˙(s)ds is diﬀerentiable in t∈[0,T]. In this case the scalar product in H satisﬁes hh,giH =hK∗h,K∗gi=hh,Γgi, where Γ=KK∗ and K∗ is the adjoint of K with respect to hh,gi:=hh,˙ g˙i L2([0,T],dt); see [1]. Moreover, for any orthonormal basis (hk)k∈N of H, we have the expansion Xt = X∞ k=0 hχt,hkiHX(h”