A Note on Euler Approximations for Stochastic Differential Equations with Delay

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.

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Correspondence to Sotirios Sabanis.

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Gyöngy, I., Sabanis, S. A Note on Euler Approximations for Stochastic Differential Equations with Delay. Appl Math Optim 68, 391–412 (2013). https://doi.org/10.1007/s00245-013-9211-7

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Keywords

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