Stochastic differential equations with time-delayed feedback and multiplicative noise

Abstract

The stochastic differential equation $\dot{x}(t)=ax(t)+bx(t-\tau )+cx(t)\xi (t)$ with a time-delayed feedback and a multiplicative Gaussian noise is shown to be related to Kardar-Parisi-Zhang universality class of growing surfaces.

11 pages, 4 figures