  We propose a novel method to solve a chemical diffusion master equation of
birth and death type. This is an infinite system of Fokker-Planck equations
where the different components are coupled by reaction dynamics similar in form
to a chemical master equation. This system was proposed in [3] for modelling
the probabilistic evolution of chemical reaction kinetics associated with
spatial diffusion of individual particles. Using some basic tools and ideas
from infinite dimensional Gaussian analysis we are able to reformulate the
aforementioned infinite system of Fokker-Planck equations as a single evolution
equation solved by a generalized stochastic process and written in terms of
Malliavin derivatives and differential second quantization operators. Via this
alternative representation we link certain finite dimensional projections of
the solution of the original problem to the solution of a single partial
differential equations of Ornstein-Uhlenbeck type containing as many variables
as the dimension of the aforementioned projection space.
