Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution

Abstract

In this paper the extension of the Path Integral to non-linear systems driven by Poissonian White Noise process is presented. It is shown that at the limit when the time increment becomes infinitesimal the Kolmogorov-Feller equation is fully restored. Applications to linear and non-linear systems with different distribution of the Dirac’s deltas occurrences are performed and results are compared with analytical solution (when available) and Monte-Carlo simulation.