SMALL-FLUCTUATION EXPANSION OF THE TRANSITION-PROBABILITY FOR A DIFFUSION PROCESS

In many applications of diffusion processes, fluctuations can be consi dered as a small perturbation of the underlying deterministic dynamics . These situations are currently believed to be described by an asympt otic expansion of the corresponding transition probability in powers o f the (small) diffusion coefficient. We offer a systematic procedure w hereby all further terms in the above expansion can be systematically computed in terms of the solutions to certain Lagrange equations assoc iated with the underlying deterministic dynamics.