Perturbation theory of SDEs

Question

I am looking for some kind of perturbation theory for approximating solutions to stochastic differential equations like \begin{equation} dX_t =\mu(X_t,t) dt + \sigma(X_t,dt) dW_t \end{equation} with respect to a Wiener process $dW_t$, but I haven't found any literature on the topic. My first thought was to introduce a small parameter $\varepsilon$ into the stochastic part: \begin{equation} dX_t =\mu(X_t,t) dt + \varepsilon\sigma(X_t,dt) dW_t \end{equation} then solve the equation for the case $\varepsilon = 0$ \begin{equation} dX_t = \mu(X_t,t)dt \end{equation} and letting this solution be $X_{t,0}$, and then inserting this into the stochastic part as follows \begin{equation} dX_{t,1} =\mu(X_{t,1},t) dt + \sigma(X_{t,0},dt) dW_t \end{equation} In order to create a recursion that uses the previous solution $X_{t,n-1}$ as the stochastic volatility $\sigma(X_t,t)$ for the next SDE involving $X_{t,n}$. Is this approach valid? And does anyone know anything about stochastic perturbation methods?