# How to solve this stochastic differential equation, $dx_t=\mu dt+(\sigma-\bar{\sigma}x_t)dW_t$?

I have this stochastic differential equation which I would like to solve:

$$dx_t=\mu dt+(\sigma-\bar{\sigma}x_t)dW_t$$

It is similar to the mean-reverting process, but variance-reverting kind. No such simple solving method exists as far as I tried.

• It's a particular case of a linear SDE and there a standard techniques to solve such SDEs... you will find several related questions if you search for "linear SDE", e.g. this one. – saz Aug 29 '18 at 20:13