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Noise Sensitivity of Functionals of Fractional Brownian Motion Driven Stochastic Differential Equations: Results and Perspectives

  • Alexandre Richard
  • Denis TalayEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 208)

Abstract

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 \(\{X^H_t\}_{t\in \mathbb {R}_+}\) and of the Laplace transform of the first passage time of \(X^H\) at a given threshold. Our technique requires to extend already known Gaussian estimates on the density of \(X^H_t\) to estimates with constants which are uniform w.r.t. t in the whole half-line \(\mathbb {R}_+-\{0\}\) and H when H tends to \(\tfrac{1}{2}\).

Keywords

Fractional Brownian motion First hitting time Malliavin calculus 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.INRIASophia-AntipolisFrance

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