Noise sensitivity of functionals of fractional Brownian motion driven stochastic differential equations: Results and perspectives
Résumé
We present an innovating sensitivity analysis for stochastic differential equations: We study the sensitivity, when the Hurst parameter H of the driving fractional Brownian motion tends to the pure Brownian value, of probability distributions of smooth functionals of the trajectories of the solutions {XHt}t∈R+ and of the Laplace transform of the first passage time of XH at a given threshold. We also present an improvement of already known Gaussian estimates on the density of XHt to estimates with constants which are uniform w.r.t. t in the whole half-line R+∖{0} and w.r.t. H when H tends to 12.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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