\[euler\_hms\_thm\] and \[euler\_hoelder\] have any consequences for the other examples? Unfortunately not: for the Heston, Ait-Sahalia and 3/2-models, no linear growth condition is satisfied. Even worse, for the Ait-Sahalia model and the 3/2-model the moments of the Euler scheme explode! In the case of the 3/2-model the latter can be deduced from the following Theorem, which was obtained by Hutzenthaler, Jentzen & Kloeden in [@HMS1].

\[ref\_euler\_mom\_exp\] Let $a,b: {\mathbb R}\rightarrow {\mathbb R}$ and assume that the one-dimensional SDE $$dX_t = a(X_t)\,dt + b(X_t)\,dW_t, \quad t \in [0,T],
\qquad
X_0 = x_0 \in \mathbb{R}$$ has a unique strong solution with $$\sup_{t \in [0,T]} \mathbb{E} | X_t |^p
< \infty$$ for one $p \in [1,\infty)$. Moreover, let $b(x_0) \neq 0$ and let $ C \geq 1 $, $ \beta > \alpha > 1 $ be constants such that $$ \max\!\big(\left| a(x) \right|,
 \left| b(x) \right|
 \big) \geq 
 \frac{1}{C} \cdot 
   \left| x \right|^{\beta}
 \quad
  \text{and}
 \quad
 \min\!\big(\left| a(x) \right|,
 \left| b(x) \right|
 \big) \leq 
 C \cdot  | x |^{\alpha}$$ for all $ |x| \geq C $. Then, the corresponding Euler scheme ${ \overline{X}}^n$ with stepsize $\Delta=T/n$ satisfies $$\label{eq:euler_divergence}
  \lim_{n \rightarrow \infty}
  \mathbb{E}
    |X_T - { \overline{X}}^n_{T}|^p= \infty
  \quad
  \text{and}
  \quad
  \lim_{n \rightarrow \infty}
  