  Both stochastic and PDE modeling approaches have been used and compared in
various context in biology. Typically, stochastic models are easier to
parameterize, can be used to integrate underlying biological phenomena, but
hard to analyze mathematically and usually computational expensive. PDE models
are amenable to mathematical analysis and computational methods are
well-developed, but biological processes are usually lumped together in them
and parameters harder to obtain. Therefore it is important to find connections
of different approaches. In this note, I give some investigation of methods to
derive a Chapman-Kolmogorov type PDE model from a stochastic hybrid system,
highlighting the close connection between these two.

Probability