Thanks! Your comment is helpful.
I saw references to “jump processes” and “Markov jump processes” in finance. I think that may be what I have.
I think such process could be described by a regime switching model mentioned here: Stochastic Volatility with Jump Diffusion?. Original model description in Stan: http://modernstatisticalworkflow.blogspot.ch/2018/02/regime-switching-models-in-stan.html. Defined here is PyMC: https://github.com/junpenglao/Planet_Sakaar_Data_Science/blob/master/Ports/Regime-switching%20models%20in%20PyMC3.ipynb.
Do you think I am on the right track?