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

#### 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.
##### Scheda breve Scheda completa Scheda completa (DC)
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
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10447/58994`
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