A Note on Euler Approximations for Stochastic Differential Equations with Delay

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Abstract

An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure convergence is obtained under local Lipschitz and also under monotonicity conditions.
Original languageEnglish
Pages (from-to)391-412
JournalApplied Mathematics and Optimization
Volume68
Issue number3
Early online date24 Aug 2013
DOIs
Publication statusPublished - Dec 2013

Keywords

  • Stochastic delay differential equations
  • Euler approximations
  • Rate of convergence
  • Local Lipschitz condition
  • Monotonicity condition

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