有界可测函数随机微分时滞方程的弱逼近

Q1 Mathematics

Lms Journal of Computation and Mathematics Pub Date : 2013-01-01 DOI:10.1112/S1461157013000120

Hua Zhang

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引用次数: 3

摘要

本文研究了E [φ (y (T))]对E [φ (x (T))]的弱逼近问题，其中x (T)是随机微分时滞方程的解，y (T)由欧拉格式定义。对于φ∈C 3b, Buckwar, Kuske, Mohammed and Shardlow(“随机微分时滞方程的欧拉格式的弱收敛性”，LMS J.计算机学报。数学。11(2008)60-69)已经证明欧拉格式具有弱收敛阶1。这里我们证明了当φ仅在附加的非退化条件下被假设为可测且有界时，同样的结果成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Weak approximation of stochastic differential delay equations for bounded measurable function

In this paper we study the weak approximation problem of E [ φ ( x ( T ))] by E [ φ ( y ( T ))], where x ( T ) is the solution of a stochastic diﬀerential delay equation and y ( T ) is deﬁned by the Euler scheme. For φ ∈ C 3 b , Buckwar, Kuske, Mohammed and Shardlow (‘Weak convergence of the Euler scheme for stochastic diﬀerential delay equations’, LMS J. Comput. Math. 11 (2008) 60–69) have shown that the Euler scheme has weak order of convergence 1. Here we prove that the same results hold when φ is only assumed to be measurable and bounded under an additional non-degeneracy condition.

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来源期刊

Lms Journal of Computation and Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.