کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4609215 1338440 2006 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Optimal approximation of SDE's with additive fractional noise
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Optimal approximation of SDE's with additive fractional noise
چکیده انگلیسی

We study pathwise approximation of scalar stochastic differential equations with additive fractional Brownian noise of Hurst parameter , considering the mean square L2-error criterion. By means of the Malliavin calculus we derive the exact rate of convergence of the Euler scheme, also for non-equidistant discretizations. Moreover, we establish a sharp lower error bound that holds for arbitrary methods, which use a fixed number of bounded linear functionals of the driving fractional Brownian motion. The Euler scheme based on a discretization, which reflects the local smoothness properties of the equation, matches this lower error bound up to the factor 1.39.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 22, Issue 4, August 2006, Pages 459-474