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math.PR2007★ 1 cited
Asymptotic expansions at any time for scalar fractional SDEs with Hurst index
Sébastien Darses, Ivan Nourdin
We study the asymptotic expansions with respect to of \[\mathrm{E}[Δ_hf(X_t)],\qquad \mathrm{E}[Δ_hf(X_t)|\mathscr{F}^X_t]\quadand\quad \mathrm{E}[Δ_hf(X_t)|X_t],\] where $Δ_hf…
math.PR2007
Differentiating sigma-fields for Gaussian and shifted Gaussian processes
Sébastien Darses, Ivan Nourdin, Giovanni Peccati
We study the notions of differentiating and non-differentiating sigma-fields in the general framework of (possibly drifted) Gaussian processes, and characterize their invariance pr…