On the global error of Itô--Taylor schemes for strong approximation of scalar stochastic differential equations
From the viewpoint of computational cost, the authors study the error incurred by Itô-Taylor methods for approximating the solution of the Itô stochastic differential equation \[ dX(t)= a(t, X(t))\,dt+ b(t, X(t))\,dW(t),\quad 0\leq t\leq 1. \] Two theorems on this are proved. The main result obtained is that the order of error with respect to \(N\), the number of multiple Itô integrals evaluated in applying the numerical method, is at best of order \(N^{-{1\over 2}}\).
scientific article; zbMATH DE number 2117870
scientific article