EXACT STATIONARY PROBABILITY DENSITY FOR SECOND ORDER NON-LINEAR SYSTEMS UNDER EXTERNAL WHITE NOISE EXCITATION

1997 ◽  
Vol 205 (5) ◽  
pp. 647-655 ◽  
Author(s):  
R. Wang ◽  
K. Yasuda
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Linear Systems ◽  
Second Order ◽  
Stationary Probability ◽  
Stationary Probability Density ◽  
White Noise Excitation ◽  
Non Linear ◽  
Non Linear Systems

scholarly journals Dynamics of a Nonlinear Business Cycle Model Under Poisson White Noise Excitation

2015 ◽  
Vol 3 (2) ◽  
pp. 176-183 ◽  
Author(s):  
Jiaorui Li ◽  
Shuang Li
Keyword(s):  
Business Cycle ◽  
White Noise ◽  
Economic System ◽  
Probability Density ◽  
Stationary Probability ◽  
Cycle Model ◽  
Poisson White Noise ◽  
Stationary Probability Density ◽  
White Noise Excitation ◽  
Business Cycle Model

AbstractSeveral observations in real economic systems have shown the evidence of non-Gaussianity behavior, and one of mathematical models to describe these behaviors is Poisson noise. In this paper, stationary probability density of a nonlinear business cycle model under Poisson white noise excitation has been studied analytically. By using the stochastic averaged method, the approximate stationary probability density of the averaged generalized FPK equations are obtained analytically. The results show that the economic system occurs jump and bifurcation when there is a Poisson impulse existing in the periodic economic system. Furthermore, the numerical solutions are presented to show the effectiveness of the obtained analytical solutions.

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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