A PARTIAL DIFFERENTIAL EQUATION FOR THE CHARACTERISTIC FUNCTION OF THE RESPONSE OF NON-LINEAR SYSTEMS TO ADDITIVE POISSON WHITE NOISE

1996 ◽  
Vol 198 (2) ◽  
pp. 193-202 ◽  
Author(s):  
M. Grigoriu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Characteristic Function ◽  
White Noise ◽  
Linear Systems ◽  
Partial Differential ◽  
Poisson White Noise ◽  
Non Linear ◽  
Non Linear Systems

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.

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.

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