Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Hölder continuity in the Hurst parameter of functionals of Stochastic Differential Equations driven by fractional Brownian motion

Alexandre Richard 1 Denis Talay 1
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : In this paper we develop sensitivity analyses w.r.t. the long-range/memory noise parameter for solutions to stochastic differential equations and the probability distributions of their first passage times at given thresholds. Here we consider the case of stochastic differential equations driven by fractional Brownian motions and the sensitivity , when the Hurst parameter $H$ of the noise tends to the pure Brownian value, of probability distributions of certain functionals of the trajectories of the solutions $\{X^H_t\}_{t\in \mathbb{R}_+}$. We first get accurate sensitivity estimates w.r.t. $H$ around the critical Brownian parameter $H = \tfrac{1}{2}$ of time marginal probability distributions of $X^H$. We second develop a sensitivity analysis for the Laplace transform of first passage time of $X^H$ at a given threshold. Our technique requires accurate Gaussian estimates on the density of $X^H_t$. The Gaussian estimate we obtain in Section 5 may be of interest by itself.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [28 references]  Display  Hide  Download

https://hal.inria.fr/hal-01323288
Contributor : Alexandre Richard <>
Submitted on : Monday, May 30, 2016 - 4:57:12 PM
Last modification on : Tuesday, May 18, 2021 - 2:32:02 PM

Links full text

Identifiers

  • HAL Id : hal-01323288, version 1
  • ARXIV : 1605.03475

Citation

Alexandre Richard, Denis Talay. Hölder continuity in the Hurst parameter of functionals of Stochastic Differential Equations driven by fractional Brownian motion. 2016. ⟨hal-01323288⟩

Share

Metrics

Record views

414