Equivalent linearization for systems driven by Lévy white noise

Abstract

The equivalent linearization method is extended to the case of nonlinear systems driven by Lévy white noise. The classical objective function used for the determination of the equivalent linear system cannot be applied because the Lévy process generating the Lévy white noise has no variance and higher order moments. An alternative objective function based on the characteristic function of the state of the linear system is used for solution. Two simple examples are presented to illustrate the proposed extension of the equivalent linearization method. The examples show that the proposed equivalent linearization method provides approximations of quality similar to the classical equivalent linearization method.