On the boundedness of asymptotic stability regions for the stochastic theta method

A. Bryden, D.J. Higham

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

The stochastic theta method gives a computational procedure for simulating ordinary stochastic differential equations. The method involves a free parameter, THgr. Here, we characterise the precise value of THgr beyond which the region of linear asymptotic stability of the method becomes unbounded. The cutoff point is seen to differ from that in the deterministic case. Computations that suggest further results are also given.
LanguageEnglish
Pages1-7
Number of pages7
JournalBIT Numerical Mathematics
Volume43
Issue number1
DOIs
Publication statusPublished - Mar 2003

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θ-method
Stability Region
Asymptotic stability
Asymptotic Stability
Boundedness
Differential equations
Stochastic Ordinary Differential Equations
Linear Stability

Keywords

  • almost sure stability
  • Euler-Maruyama
  • multiplicative noise
  • stochastic equations
  • differential equations

Cite this

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On the boundedness of asymptotic stability regions for the stochastic theta method. / Bryden, A.; Higham, D.J.

In: BIT Numerical Mathematics, Vol. 43, No. 1, 03.2003, p. 1-7.

Research output: Contribution to journalArticle

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KW - multiplicative noise

KW - stochastic equations

KW - differential equations

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