Weak consistency of the Euler method for numerically solving stochastic differential equations with discontinuous coefficients

被引：25

作者：

Chan, KS ^{[1
]}

Stramer, O ^{[1
]}

机构：

[1] Univ Iowa, Dept Stat & Actuarial Sci, Iowa City, IA 52242 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1998年 / 76卷 / 01期

基金：

美国国家科学基金会;

关键词：

good integrators; Martingale differences; threshold ARMA processes;

D O I：

10.1016/S0304-4149(98)00020-9

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove that, under appropriate conditions, the sequence of approximate solutions constructed according to the Euler scheme converges weakly to the (unique) solution of a stochastic differential equation with discontinuous coefficients. We also obtain a sufficient condition for the existence of a solution to a stochastic differential equation with discontinuous coefficients. These results are then applied to justify the technique of simulating continuous-time threshold autoregressive moving-average processes via the Euler scheme. (C) 1998 Elsevier Science B.V. All rights reserved.

引用

页码：33 / 44

页数：12

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