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.

  • $\begingroup$ 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. $\endgroup$ – saz Aug 29 '18 at 20:13

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