I am looking for some ideas (or references) in order to get an explicit SDE (if it exists) which would have a stylised property extending in some sense the mean-reversion property of SDE of Ornstein-Uhlenbeck type.
More formally, is it possible to have a $n$-means reverting process defined by an SDE ?
I imagine this SDE would have the form like $dS_t=f_1(S_t,t)dt+...+f_n(S_t,t)dt+\sigma dW_t$
where $f_i$'s are such that if $S_t$ is closed to i-th mean $m_i$ then it stays closed to this point with high probability.
I am sorry to not define the necessary concepts more clearly but as I am only looking for ideas (or refernces) on this, I rather define some intuitive concept than a fully formal framework in order not to close any possibility.
Thank's for the time spend reading those lines
PS : I would like to avoid the n states regime switching technology if possible