Let x stochastic variable. Clearly and we find We next generalize to take the limit and write the Langevin equation on the form where and with the Dirac -function. Noise with these properties called white . Find Restrict t to small value . Get jump moments Higher order jump moments of higher order in .
L is a process with discrete jumps.
If noise external Open system. There is always a nonzero relaxation time. For additive white Gaussian noise Langevin equation equivalent to Fokker-Planck equation. When noise nonlinear need to impose interpretation. Ito and Stratanovich interpretation most common.