A note on Euler approximations for stochastic differential equations   with delay
  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. 
Istvan Gy\"ongy and Sotirios Sabanis
math.PR