### Abstract

A method for the evaluation of the probability density function (p.d.f.) of the response process of non-linear systems under external stationary Poisson white noise excitation is presented. The method takes advantage of the great accuracy of the Monte Carlo simulation (MCS) in evaluating the first two moments of the response process by considering just few samples. The quasi-moment neglect closure is used to close the infinite hierarchy of the moment differential equations of the response process. Moreover, in order to determine the higher order statistical moments of the response, the second-order probabilistic information given by MCS in conjunction with the quasi-moment neglect closure leads to a set of linear differential equations. The quasi-moments up to a given order are used as partial probabilistic information on the response process in order to find the p.d.f. by means of the C-type Gram–Charlier series expansion.

Original language | English |
---|---|

Pages (from-to) | 1269-1283 |

Number of pages | 15 |

Journal | International Journal of Nonlinear Mechanics |

Volume | 38 |

Issue number | 8 |

Publication status | Published - 2003 |

### Keywords

- Non-linear stochastic dynamics
- Stationary Poisson process
- Monte Carlo simulation
- Non-Gaussian probability density function
- Quasi-moment neglect closure

## Fingerprint Dive into the research topics of 'Monte Carlo simulation in the stochastic analysis of non-linear systems under external stationary Poisson white noise input'. Together they form a unique fingerprint.

## Cite this

Muscolino, G., Ricciardi, G., & Cacciola, P. (2003). Monte Carlo simulation in the stochastic analysis of non-linear systems under external stationary Poisson white noise input.

*International Journal of Nonlinear Mechanics*,*38*(8), 1269-1283.