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 $\lambda$-Hölder continuous process, $\lambda \in (0,1)$. We prove that, under some mild moment assumptions on the Hölder constant of the noise, the $L^r(\Omega ;L^{\infty }([0,T]))$-rate of convergence is equal to $\lambda$. To exemplify, we consider numerical schemes for the generalized Cox--Ingersoll-Ross and Tsallis--Stariolo--Borland models. The results are illustrated by simulations.

24 pages, 3 figures