TY - CONF

T1 - Nonlinear SDE Excited by External Lévy White Noise Processes

AU - Cottone, Giulio

PY - 2010

Y1 - 2010

N2 - 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. Thisapproach 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.

AB - 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. Thisapproach 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.

KW - Convolution quadrature: Lévy white noise

KW - Generalized fractional calculus

KW - Non-polynomial drift.

KW - Stochastic differential equations

KW - Convolution quadrature: Lévy white noise

KW - Generalized fractional calculus

KW - Non-polynomial drift.

KW - Stochastic differential equations

UR - http://hdl.handle.net/10447/58994

UR - http://rpsonline.com.sg/proceedings/9789810876197/html/cont.html

M3 - Other

ER -