Non-Linear Systems Driven by White Noise Processes and Handled by the Characteristic Function Equations

2009 ◽  
Author(s):  
M. Di Paola ◽  
G. Cottone
Keyword(s):  
Characteristic Function ◽  
White Noise ◽  
Linear Systems ◽  
Non Linear ◽  
Non Linear Systems

Measurement of Wiener kernels

1984 ◽  
Vol 16 (1) ◽  
pp. 11-12
Author(s):  
Yoshifusa Ito
Keyword(s):  
Differential Operator ◽  
Mathematical Models ◽  
White Noise ◽  
Linear Systems ◽  
Main Part ◽  
The Other ◽  
Linear Functionals ◽  
Wiener Kernels ◽  
Non Linear ◽  
Non Linear Systems

Since the late 1960s Wiener's theory on the non-linear functionals of white noise has been widely applied to the construction of mathematical models of non-linear systems, especially in the field of biology. For such applications the main part is the measurement of Wiener's kernels, for which two methods have been proposed: one by Wiener himself and the other by Lee and Schetzen. The aim of this paper is to show that there is another method based on Hida's differential operator.

Probabilistic criterion for Gausian equivalent linearization

1996 ◽  
Vol 18 (2) ◽  
pp. 1-6
Author(s):  
N. D. Anh ◽  
W. Schiehlen
Keyword(s):  
White Noise ◽  
Linear Systems ◽  
Equivalent Linearization ◽  
Stationary Response ◽  
Probabilistic Criterion ◽  
Non Linear ◽  
Equivalent Equation ◽  
Non Linear Systems

Within the scope of Gaussian equivalent linearization, a new probabilistic criterion for determining the coefficients of the linearized equivalent equation is proposed to treat stationary response of non-linear systems under zero mean Gaussian ro.nd.om excitation. Application to the Duffing oscillate subjected to white noise is presented that shows significant improvement over corresponding accuracy of the classical Gaussian equivalent linearization for both weak and strong non-linear.

Non Linear Systems Under Complex α-Stable Le´vy White Noise

2003 ◽  
Author(s):  
M. Di Paola ◽  
M. Vasta
Keyword(s):  
Nonlinear Systems ◽  
Characteristic Function ◽  
White Noise ◽  
Linear Systems ◽  
Poisson White Noise ◽  
Input And Output ◽  
Non Linear Systems ◽  
Linear And Nonlinear ◽  
White Noises ◽  
Linear And Nonlinear Systems

The problem of predicting the response of linear and nonlinear systems under Le´vy white noises is examined. A method of analysis is proposed based on the observation that these processes have impulsive character, so that the methods already used for Poisson white noise or normal white noise may be also recast for Le´vy white noises. Since both the input and output processes have no moments of order two and higher, the response is here evaluated in terms of characteristic function.

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