Detect and Diagnose Unexpected Changes in the Output Probability Density Functions for Dynamic Stochastic Systems: An Identification Based Approach

1999 ◽  
Vol 32 (2) ◽  
pp. 7897-7902
Author(s):  
H. Wang ◽  
Q.H. Wu
Keyword(s):  
Probability Density ◽  
Stochastic Systems ◽  
Probability Density Functions ◽  
Density Functions ◽  
Dynamic Stochastic ◽  
Output Probability

scholarly journals A description of stochastic systems using chaotic maps

2004 ◽  
Vol 2004 (2) ◽  
pp. 137-141 ◽  
Author(s):  
Abraham Boyarsky ◽  
Pawel Góra
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Probability Density ◽  
Stochastic Systems ◽  
Chaotic Maps ◽  
Probability Density Functions ◽  
Density Functions ◽  
Partial Differential ◽  
The Family ◽  
Point Transformations

Let ρ(x,t) denote a family of probability density functions parameterized by time t. We show the existence of a family {τ1:t>0} of deterministic nonlinear (chaotic) point transformations whose invariant probability density functions are precisely ρ(x,t). In particular, we are interested in the densities that arise from the diffusions. We derive a partial differential equation whose solution yields the family of chaotic maps whose density functions are precisely those of the diffusion.

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