کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4626259 | 1631784 | 2015 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Optimal global approximation of SDEs with time-irregular coefficients in asymptotic setting
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We investigate strong approximation of solutions of scalar stochastic differential equations (SDEs) with irregular coefficients. In PrzybyÅowicz (2015) [23], an approximation of solutions of SDEs at a single point is considered (such kind of approximation is also called a one-point approximation). Comparing to that article, we are interested here in a global reconstruction of trajectories of the solutions of SDEs in a whole interval of existence. We assume that a drift coefficient a:[0,T]ÃRâR is globally Lipschitz continuous with respect to a space variable, but only measurable with respect to a time variable. A diffusion coefficient b:[0,T]âR is only piecewise Hölder continuous with Hölder exponent ϱ â (0, 1]. The algorithm and results concerning lower bounds from PrzybyÅowicz (2015) [23] cannot be applied for this problem, and therefore we develop a suitable new technique. In order to approximate solutions of SDEs under such assumptions we define a discrete type randomized Euler scheme. We provide the error analysis of the algorithm, showing that its error is O(nâmin{ϱ,1/2}). Moreover, we prove that, roughly speaking, the error of an arbitrary algorithm (for fixed a and b) that uses n values of the diffusion coefficient, cannot converge to zero faster than nâmin{ϱ,1/2} as nâ+â. Hence, the proposed version of the randomized Euler scheme achieves the established best rate of convergence.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 270, 1 November 2015, Pages 441-457
Journal: Applied Mathematics and Computation - Volume 270, 1 November 2015, Pages 441-457
نویسندگان
PaweÅ PrzybyÅowicz,