  Motivated by applications in systems biology, we seek a probabilistic
framework based on Markov processes to represent intracellular processes. We
review the formal relationships between different stochastic models referred to
in the systems biology literature. As part of this review, we present a novel
derivation of the differential Chapman-Kolmogorov equation for a general
multidimensional Markov process made up of both continuous and jump processes.
We start with the definition of a time-derivative for a probability density but
place no restrictions on the probability distribution, in particular, we do not
assume it to be confined to a region that has a surface (on which the
probability is zero). In our derivation, the master equation gives the jump
part of the Markov process while the Fokker-Planck equation gives the
continuous part. We thereby sketch a {}``family tree'' for stochastic models in
systems biology, providing explicit derivations of their formal relationship
and clarifying assumptions involved.
