White Noise Processes

A class of white noise processes defined as the formal derivative of Lévy processes is studied. It is shown that (1) This class consists of two types of processes, the Gauss white noise and the Poisson white noise; (2) there are no other white noise processes of practical interest whose probability law can be specified simply; (3) delta correlated processes used in random vibration analyses to model non‐Gaussian wide band processes seem to be Poisson white noises; and (4) it is not possible to obtain non‐Gaussian white noises from Gaussian white noises by memoryless nonlinear transformations.