اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA note on the continuity in the Hurst index of the solution of rough differential equations driven by a fractional Brownian motion
75
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 $H in (1/3, 1/2]$.
قيم البحث
اقرأ أيضاً
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 cas
e 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.
We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary regime.
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
oellipticity condition, we establish a sharp local estimate on the associated control distance function and a sharp local lower estimate on the density of the solution. Our methodology relies heavily on the rough paths structure of the equation.
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 ell
ipticity condition, we establish a sharp local estimate on the associated control distance function and a sharp local lower estimate on the density of the solution.
In this presentation, we introduce a new method for change point analysis on the Hurst index for a piecewise fractional Brownian motion. We first set the model and the statistical problem. The proposed method is a transposition of the FDpV (Filtered
Derivative with p-value) method introduced for the detection of change points on the mean in Bertrand et al. (2011) to the case of changes on the Hurst index. The underlying statistics of the FDpV technology is a new statistic estimator for Hurst index, so-called Increment Bernoulli Statistic (IBS). Both FDpV and IBS are methods with linear time and memory complexity, with respect to the size of the series. Thus the resulting method for change point analysis on Hurst index reaches also a linear complexity.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
