I have an equation of the form:
$$dX_t=\mu(X_t)X_tdt+\sigma(X_t)X_tdZ_t+dL_t, \quad X_0=x_0\in (0,a]$$
where, $L_t$ is the reflection function (as in Skorokhod, 1961). This reflection does not allow the process to get past a barrier $a>0$. Therefore, this process is always between 0 and $a$.
While I was able to find many results concerning the structure I must impose on the coefficients $\mu(\cdot)$ and $\sigma(\cdot)$ to get strong solutions, pathwise uniqueness, weak solutions and so on for processes without a reflecting barrier, I was unable to find much on processes with reflection.
Does anyone know a good reference for this kind of processes?