S. Sandow et S. Trimper, GAUSSIAN WHITE-NOISE AS A MANY-PARTICLE PROCESS - THE KARDAR-PARISI-ZHANG EQUATION, Journal of physics. A, mathematical and general, 26(13), 1993, pp. 3079-3084
A new approach is proposed to derive a stochastic differential equatio
n from a Master equation. Starting from the Liouvillian in a Fock spac
e formulation and using a functional integral representation in terms
of coherent states we get the corresponding Langevin equation. As exam
ples aggregation and segregation processes with different probability
rates are analysed. In the case of a state dependent growth rate it re
sults in a generalized Kardar-Parisi-Zhang equation 7! including the
kind of noise which is a purely Gaussian one in this model.