Given a discrete stochastic process, for example a chemical reaction system or a birth and death process, we often want to find a continuous stochastic approximation so that the techniques of stochastic differential equations may be brought to bear. One powerful and useful way to do this is the system size expansion of van Kampen to express a trajectory as a small stochastic perturbation to a d...

We consider an Ito stochastic differential equation with delay, driven by brownian motion, whose solution, by an appropriate reformulation, defines a Markov process X with values in a space of continuous functions C, with generator L. We then consider a backward stochastic differential equation depending on X , with unknown processes (Y, Z), and we study properties of the resulting system, in p...