The convergence of the split-step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven in -sense. Almost sure convergence is derived from the convergence by Chebyshev’s inequality and the Borel-Cantelli lemma; meanwhile, the convergence rate is obtained.
"Almost Sure and Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/390418