Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises

Abstract

In this paper, we analyze the drift-implicit (or backward) Euler numerical scheme for a class of stochastic differential equations with unbounded drift driven by an arbitrary λ-Hölder continuous process, λ ∈ (0,1). We prove that, under some mild moment assumptions on the Hölder constant of the noise, the L^{r}({Omega };L^{infty }([0,T]))-approximation error converges to 0 as O(Δλ), Δ → 0. To exemplify, we consider numerical schemes for the generalized Cox–Ingersoll–Ross and Tsallis–Stariolo–Borland models. The results are illustrated by simulations.