In this paper, the widely known path integral method, derived from the application of the
Chapman–Kolmogorov equation, is described in details and discussed with reference to the …

Recovering the probability distribution of the performance function with an arbitrary shape is
still a difficult task for structural reliability analysis. Since working with the characteristic …

An efficient method for reliability assessment of structural dynamic systems is proposed. In
the proposed method, the reliability is evaluated by the equivalent extreme value distribution …

In this paper the solution of the Fokker Planck (FPK) equation in terms of (complex) fractional
moments is presented. It is shown that by using concepts coming from fractional calculus …

An analytical method based on complex fractional moments (CFMs) is presented to obtain
the transient response probability density of a dynamic system with nonlinearity in both …

In this paper, the probabilistic characterization of a nonlinear system enforced by Poissonian
white noise in terms of complex fractional moments (CFMs) is presented. The main …

In this paper, the transient response of the time-delay system under additive and
multiplicative Gaussian white noise is investigated. Based on the approximate …

In this paper a novel procedure is developed for evolutionary power spectra (EPS)
estimation of univariate nonstationary stochastic processes. Specifically, the EPS is …

This paper studies the transient response of the nonlinear system with Gaussian colored
noise. The one-dimensional Itô stochastic differential equation with respect to amplitude …

The probability density evolution method is renowned for its effectiveness in conducting
stochastic seismic response analyses of structures with uncertain parameters. Within this …