Drift-implicit Euler scheme for sandwiched processes driven by H\"older noises

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 $\lambda$-H"older continuous process, $\lambda \in (0,1)$. We prove that, under some mild moment assumptions on the H"older constant of the noise, the $L^r(\mathrm{\Omega };L^{\mathrm{\infty }}([0,T]))$-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.