  Spatially dependent birth-death processes can be modelled by kinetic models
such as the BBGKY hierarchy. Diffusion in infinite dimensional systems can be
modelled with Brownian motion in Hilbert space. In this work Doi field
theoretic formalism is utilised to establish dualities between these classes of
processes. This enables path integral methods to calculate expectations of
duality functions. These are exemplified with models ranging from stochastic
cable signalling to jump-diffusion processes.
