Random response of a simple system with stochastic uncertainty and noise in parameters

The paper is concerned with the analysis of simultaneous effect a random perturbation and white noise in coefficient system on its response. excitation 1st order described by sum deterministic signal additive noise, which partly correlated parametric noise. parameter considered statistics set realizations. It reveals that probability density these perturbations must be limited phase space, otherwise would lose stochastic stability probability, either immediately or after certain time. width permissible zone depends intensity extent correlation type density. general explanation demonstrated cases normal, uniform, truncated normal densities.