Ornstein-Uhlenbeck like process for non-normal data distributions

Question

I have a set of data which histogram looks like this:

The values are not normally distributed since the distribution is not simetric.

For another set of data that is normally distributed, I have used a Ornstein-Uhlenbeck stochastic process to generate representative values.

Since OU processes only work with normally distributed data, what can I use to represent the depicted data set?

Thanks.