Almost sure exponential stability of numerical solutions for stochastic delay differential equations

Fuke Wu, Xuerong Mao, Lukasz Szpruch

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Abstract

Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the Borel–Cantelli lemma.
Original languageEnglish
Pages (from-to)681-697
Number of pages17
JournalNumerische Mathematik
Volume115
Issue number4
DOIs
Publication statusPublished - Jun 2010

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Keywords

  • numerical solutions
  • stochastic delay
  • differential equations

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