Nonlinear SDE Excited by External Lévy White Noise Processes

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    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.
    Lingua originaleEnglish
    Stato di pubblicazionePublished - 2010

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    White noise
    Statistics
    Characteristic Function
    Convolution
    Nonlinear Stochastic Systems
    Quadrature Method
    System of Differential Equations
    Integral Operator
    Quadrature
    Governing equation
    Partial differential equation
    Linear Systems
    Numerical Methods
    Differential equation
    Polynomial
    Term
    Operator

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    @conference{e99cd7bd9d02486a87608afc31aea1f2,
    title = "Nonlinear SDE Excited by External L{\'e}vy 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.",
    keywords = "Convolution quadrature: L{\'e}vy white noise; Generalized fractional calculus; Stochastic differential equations; Non-polynomial drift.",
    author = "Giulio Cottone",
    year = "2010",
    language = "English",

    }

    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. 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.

    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. 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.

    KW - Convolution quadrature: Lévy white noise; Generalized fractional calculus; Stochastic differential equations; Non-polynomial drift.

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

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

    M3 - Paper

    ER -