A suggested modification of noise theory

A class of stationary, equilibrium, Markoff processes is demonstrated all of which have the same equilibrium distribution, ${W_0}\left ( x \right )$, and correlation function $R\left ( t \right ) = {E_0}\exp \left ( { - t/{\tau _0}} \right )$ differing from each other in the number of zero crossings of the system per second. The processes are described by an integral equation characterized by a parameter $\gamma$. As $\gamma$ approaches 1, the integral equation passes over into the Fokker-Planck equation ${\tau _0}\frac {{\partial W}}{{\partial t}} = {E_0}\frac {{{\partial ^2}W}}{{\partial {x^2}}} + \frac {\partial }{{\partial x}}\left ( {xW} \right )$. Since the number of zero crossings per second of the system becomes infinite as $\gamma$ goes to one, the degenerate nature of the Fokker-Planck process is made evident.