On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions

机译：具有二维空间强逼近的具有任意慢收敛速度的随机微分方程

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In a recent article (Jentzen et al. 2016 Commun. Math. Sci. >14, 1477–1500 ()), it has been established that, for every arbitrarily slow convergence speed and every natural number d∈{4,5,…}, there exist d-dimensional stochastic differential equations with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence. In this paper, we strengthen the above result by proving that this slow convergence phenomenon also arises in two (d=2) and three (d=3) space dimensions.

机译：在最近的一篇文章（Jentzen等人，2016 Commun。Math。Sci。> 14 ，1477–1500（））中，已经确定，对于每个任意慢的收敛速度和每个自然数d∈ {4,5，…}，存在具有无限常可微和全局有界系数的d维随机微分方程，因此基于有限多个布朗运动驱动观测的近似方法无法以绝对均值收敛于解。给定收敛速度。在本文中，我们通过证明在两个（d = 2）和三个（d = 3）空间维中也会出现这种缓慢收敛现象，来加强上述结果。

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期刊名称 Proceedings. Mathematical Physical and Engineering Sciences
作者
Máté Gerencsér; Arnulf Jentzen; Diyora Salimova;
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作者单位

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年(卷),期 -1(473),2207
年度 -1
页码 20170104
总页数 16
原文格式 PDF
正文语种
中图分类病理学;
关键词
stochastic differential equation slow convergence rate lower error bounds smooth coefficients;

机译：随机微分方程;收敛速度慢;误差范围低;系数平滑;

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专利

1. On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions [J] . Gerencser Mate, Jentzen Arnulf, Salimova Diyora Proceedings of the Royal Society. Mathematical, physical and engineering sciences . 2017,第2207期

机译：在两个空间尺寸中具有任意慢速率的随机微分方程，具有两个空间尺寸的强近似
2. ON STOCHASTIC DIFFERENTIAL EQUATIONS WITH ARBITRARY SLOW CONVERGENCE RATES FOR STRONG APPROXIMATION [J] . Jentzen Arnulf, Mueller-Gronbach Thomas, Yaroslavtseva Larisa Communications in mathematical sciences . 2016,第6期

机译：强逼近的具有任意慢收敛速度的随机微分方程
3. Strong rate of convergence for the Euler-Maruyama approximation of one-dimensional stochastic differential equations involving the local time at point zero [J] . Mohsine Benabdallah, Kamal Hiderah Monte Carlo Methods and Applications . 2018,第4期

机译：一维随机微分方程的欧拉-丸山近似的强收敛速度，涉及零点的当地时间
4. Rate of Convergence of Wong-Zakai Approximations for Stochastic Partial Differential Equations [C] . István Gy?ngy, Pablo Raúl Stinga Seminar on Stochastic Analysis, Random Fields, and Applications . 2013

机译：随机偏微分方程的Wong-Zakai近似率的收敛速度
5. Analysis and finite element approximations of stochastic optimal control problems constrained by stochastic elliptic partial differential equations [D] . Lee, Jangwoon 2008

机译：随机椭圆偏微分方程约束的随机最优控制问题的分析和有限元逼近
6. Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations [O] . Ling Zhang -1

机译：半线性随机时滞微分方程指数Euler方法的收敛性和稳定性
7. On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions [O] . Gerencsér, Máté, Jentzen, Arnulf, Salimova, Diyora 2017

机译：关于任意慢收敛的随机微分方程两个空间维度中强近似的速率
8. Efficient Numerical Approximations of Tracking Statistical Quantities of Interest From the Solution of High-Dimensional Stochastic Partial Differential Equations. [R] . Trenchea, C. 2012

机译：基于高维随机偏微分方程解的跟踪统计量的有效数值逼近。

On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions

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