The Annals of Probability

The Euler scheme with irregular coefficients

Liqing Yan

Full-text: Open access

Abstract

Weak convergence of the Euler scheme for stochastic differential equations is established when coefficients are discontinuous on a set of Lebesgue measure zero. The rate of convergence is presented when coefficients are Hölder continuous. Monte Carlo simulations are also discussed.

Article information

Source
Ann. Probab., Volume 30, Number 3 (2002), 1172-1194.

Dates
First available in Project Euclid: 20 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1029867124

Digital Object Identifier
doi:10.1214/aop/1029867124

Mathematical Reviews number (MathSciNet)
MR1920104

Zentralblatt MATH identifier
1020.60054

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H35: Computational methods for stochastic equations [See also 65C30] 60H10: Stochastic ordinary differential equations [See also 34F05] 60H35: Computational methods for stochastic equations [See also 65C30]
Secondary: 65C05: Monte Carlo methods 60F05: Central limit and other weak theorems 68U20: Simulation [See also 65Cxx] 65C05: Monte Carlo methods 60F05: Central limit and other weak theorems 68U20: Simulation [See also 65Cxx]

Keywords
Euler scheme stochastic differential equations weak convergence rate of convergence Monte Carlo simulations

Citation

Yan, Liqing. The Euler scheme with irregular coefficients. Ann. Probab. 30 (2002), no. 3, 1172--1194. doi:10.1214/aop/1029867124. https://projecteuclid.org/euclid.aop/1029867124


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References

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  • VANCOUVER, BC CANADA V6T 1Z2 E-MAIL: ly an@pims.math.ca