Chapitre D'ouvrage Année : 2017

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}tR+ 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.
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Dates et versions

hal-01620377 , version 1 (20-10-2017)

Identifiants

Citer

Alexandre Richard, Denis Talay. Noise sensitivity of functionals of fractional Brownian motion driven stochastic differential equations: Results and perspectives. Vladimir Panov. Modern Problems of Stochastic Analysis and Statistics, Springer, pp.219-236, 2017, 978-3-319-65313-6. ⟨10.1007/978-3-319-65313-6_9⟩. ⟨hal-01620377⟩
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