Response of Linear Systems to Random Series and Filtered Poisson Processes
Mircea Dan Grigoriu · 2020
Two methods are developed for calculating mean uperossing rates and other probabilistic descriptors for the response of linear systems subject to random time series and filtered Poisson processes. The first method is based on the joint characteristic function of the response and its derivative. It is exact but complex. The second method is based on the assumption that the response can be represented by a memoryless nonlinear transformation of a Gaussian process. It involves only the marginal distribution and the covariance function of the response. Response characteristics by this method compare satisfactorily with simulation results.