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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 ${X^H_t}_{tin mathbb{R}_+}$. 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.
Within the rough path framework we prove the continuity of the solution to random differential equations driven by fractional Brownian motion with respect to the Hurst parameter $H$ when $H in (1/3, 1/2]$.
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 sm
We study the Crank-Nicolson scheme for stochastic differential equations (SDEs) driven by multidimensional fractional Brownian motion $(B^{1}, dots, B^{m})$ with Hurst parameter $H in (frac 12,1)$. It is well-known that for ordinary differential equa
In this paper, we study the reflected backward stochastic differential equations driven by G-Brownian motion with two reflecting obstacles, which means that the solution lies between two prescribed processes. A new kind of approximate Skorohod condit
This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform hyp