special case of a drift measure $\nu = \beta \, \delta_0$ where $|\beta|=1$ and $\delta_0$ denotes the Dirac measure in zero and the symmetric local time in Eq. (\[eqn:SDE\_mvd\]) the result of Corollary \[cor:reflection\_and\_absorbing\](i) was already presented in [@blei_bessel_2011], Lemma 2.24. Moreover, Corollary \[cor:non\_existence\_of\_a\_solution\] contains [@blei_bessel_2011], Lemma 2.25, which deals with the non-existence of a solution to Eq. (\[eqn:SDE\_mvd\]) with symmetric local time and drift measure $\nu = \beta \, \delta_0$ such that $|\beta|>1$.

\(ii) In W. Schmidt [@schmidt:1989] one-dimensional stochastic differential equations with reflecting barriers, more precisely, equations of the form $$\begin{aligned}
\label{eqn:SDE_refl_schmidt}
        \left\{
            \begin{aligned}
                \text{(i)}      &\phantom{=}\displaystyle X_t = X_0 + \int_0^t b(X_s) \, {\mbox{\upshape d}}B_s + L_t - R_t, \\
                \text{(ii)}     &\phantom{=}X_t \in [r_1,r_2], \\
                \text{(iii)} &\phantom{=}\text{$L_t$, $R_t$ are increasing process with $L_0 = R_0 = 0$ and} \\
                                            &\phantom{===}\begin{gathered}
                                                \int_0^t {\text{\large{$\mathds{1}$}}}_{\{r_1\}} (X_s) \, {\mbox{\upshape d}}L_s = L_t, \quad \int_0^t {\text{\large{$\mathds{1}$}}}_{\{r_2\}} (X_s) \, {\mbox{\upshape d}}R_s = R_t, \quad t \geq 0,
                                             \end{gathered}
            \end{aligned}       
        \right.
    \end{aligned}$$ where $r_1 < r_2$, were studied. Clearly, $(X,\mathbb{F})$ on $(\Omega,\mathcal{F},\mathbf{P})$ is called a solution of Eq. (\[eqn:SDE\_refl\_schmidt\]) if there exists a Wiener process $(B,\mathbb{F})$ and two processes $(L,\mathbb{F})$ and $(R,\mathbb{F})$ such that (\[eqn:SDE\_refl\_schmidt\]) is satisfied. For a solution $(X,\mathbb{F})$ of Eq. (\[eqn:SDE\_refl\_schmidt\]) it 