A numerical method for approximating the statistics of the solution of nonlinear stochastic systems excited by Gaussian and non-Gaussian external white noises is proposed. The differential equation governing the evolution in time of the characteristic function is resolved by the convolution quadrature method. This approach is especially suited for those problems in which the nonlinear drift term is not of polynomial form. In such cases the equation governing the evolution in time of the characteristic function is not a partial differential equation. Statistics are found by introducing an integral operator of Wiener-Hopf type, called the transformation operator, and applying the Lubich's convolution quadrature. This leads to find the statistics of the response by solving a linear system of differential equations.

Cottone, G. (2010). Nonlinear SDE Excited by External Lévy White Noise Processes. In Proceeding of the 6th International Conference on Computational Stochastic Mechanics. RESEARCH PUBLISHING.

Nonlinear SDE Excited by External Lévy White Noise Processes

COTTONE, Giulio
2010-01-01

Abstract

A numerical method for approximating the statistics of the solution of nonlinear stochastic systems excited by Gaussian and non-Gaussian external white noises is proposed. The differential equation governing the evolution in time of the characteristic function is resolved by the convolution quadrature method. This approach is especially suited for those problems in which the nonlinear drift term is not of polynomial form. In such cases the equation governing the evolution in time of the characteristic function is not a partial differential equation. Statistics are found by introducing an integral operator of Wiener-Hopf type, called the transformation operator, and applying the Lubich's convolution quadrature. This leads to find the statistics of the response by solving a linear system of differential equations.
Settore ICAR/08 - Scienza Delle Costruzioni
2010
6th International Conference on Computational Stochastic Mechanics
Rhodos, Grecia
13-16 Giugno 2010
CSM-6
2010
9
http://rpsonline.com.sg/proceedings/9789810876197/html/cont.html
Cottone, G. (2010). Nonlinear SDE Excited by External Lévy White Noise Processes. In Proceeding of the 6th International Conference on Computational Stochastic Mechanics. RESEARCH PUBLISHING.
Proceedings (atti dei congressi)
Cottone, G
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/58994
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact