Numerical solutions of stochastic differential delay equations under local Lipschitz condition (Q1861323)

Under certain hypotheses, which include the less restrictive assumption that \(f,g\) satisfy a local (rather than global) Lipschitz condition, a theorem is proved establishing convergence of Euler-Maruyama approximate solutions to the solution of the stochastic differential delay equation with variable delay \[ dx(t)= f\biggl(x,\bigl( \delta(t)\bigr)\biggr) dt+g\biggl(x(t), x \bigl(\delta(t) \bigr)\biggr) dB(t) \] where \(B\) is an \(m\)-dimensional Brownian motion.