Generation of bounded stochastic processes

Stationary random processes of bounded varition are generated in terms of Ito stochastic differential equations with the knowledge of their spectral densities and probability densities. The drift term in the M equation can be adjusted to match one of two types of spectral densities: the low-pass type and the narrow-band type. The diffusion term is determined according to the boundary of the random process and the shape of its probability density. It is shown that bounded random processes so generated cover a variety of profiles of probability distributionss.