Noise sensitivity of functionals of fractional Brownian motion driven stochastic differential equations: Results and perspectives

2017/02/13 by Alexandre Richard, Richard, Alexandre, Denis Talay +1
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1702.03796

arxiv created 2017/02/13 · openalex publication_date 2017/02/13 · arxiv updated 2017/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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∈ 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 in the whole half-line \R₊-\0\ and H when H tends to~\tfrac12.

Citations

• An inequality of the Hölder type, connected with Stieltjes integration

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