Exact stationary probability density functions for non-linear systems under Poisson white noise excitation

2003 ◽  
Vol 38 (4) ◽  
pp. 557-564 ◽  
Author(s):  
Carsten Proppe
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Linear Systems ◽  
Probability Density Functions ◽  
Density Functions ◽  
Stationary Probability ◽  
Poisson White Noise ◽  
Stationary Probability Density ◽  
White Noise Excitation ◽  
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.

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