NON-MARKOVIAN NOISE

The properties of non-Markovian noises with exponentially correlated m emory are discussed. Considered are dichotomic noise, white shot noise , Gaussian white noise, and Gaussian colored noise. The stationary cor relation functions of the non-Markovian versions of these noises are g iven by linear combinations of two or three exponential functions (col ored noises) or of the delta function and exponential function (white noises). The non-Markovian white noises are well defined only when the kernel of the non-Markovian master equation contains a nonzero admixt ure of a Markovian term. Approximate equations governing the probabili ty densities for processes driven by such non-Markovian noises are der ived, including non-Markovian versions of the Fokker-Planck equation a nd the telegrapher's equation. As an example, it is shown how the non- Markovian nature changes the behavior of the driven linear process.