Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation - Qian Guo; Xueyin Tao (Abstract and Applied Analysis)
The convergence of the split-step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven in Lp-sense. Almost sure convergence is derived from the Lp convergence by Chebyshev’s inequality and the Borel-Cantelli lemma; meanwhile, the convergence rate is obtained.