Stochastic Taylor Methods for Stochastic Delay Differential Equations

Authors

  • Norhayati Rosli
  • Arifah Bahar
  • Su Hoe Yeak
  • Haliza Abdul Rahman

DOI:

https://doi.org/10.11113/matematika.v29.n.597

Abstract

This paper demonstrates a systematic derivation of high order numerical methods from stochastic Taylor expansion for solving stochastic delay differential equations (SDDEs) with a constant time lag, r > 0 . The stochastic Taylor expansion of SDDEs is truncated at certain terms to achieve the order of convergence of numerical methods for SDDEs. Three different numerical schemes of Euler method, Milstein scheme and stochastic Taylor method of order 1.5 have been derived. The performance of Euler method, Milstein scheme and stochastic Taylor method of order 1.5 are investigated in a simulation study. Keywords: Numerical Solution; Stochastic Delay Differential Equations; Stochastic Taylor Expansion. 2010 Mathematics Subject Classification: 62L20; 65C20

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Published

01-06-2013

Issue

Volume 29 (June 2013) - Special Issue

Section

Analysis and Algebra

License

Copyright of articles that appear in MATEMATIKA: MJIAM belongs exclusively to Penerbit UTM Press, Universiti Teknologi Malaysia. This copyright covers the rights to reproduce the article, including reprints, electronic reproductions or any other reproductions of similar nature.

How to Cite

Stochastic Taylor Methods for Stochastic Delay Differential Equations. (2013). MATEMATIKA, 29, 241-251. https://doi.org/10.11113/matematika.v29.n.597