Online estimation algorithm for the unknown probability density functions of random parameters in auto-regression and exogenous stochastic systems

2006 ◽  
Vol 153 (4) ◽  
pp. 462-468 ◽  
Author(s):  
H. Wang ◽  
Y. Wang ◽  
A. Wang
Keyword(s):  
Probability Density ◽  
Stochastic Systems ◽  
Estimation Algorithm ◽  
Probability Density Functions ◽  
Density Functions ◽  
Random Parameters ◽  
Online Estimation ◽  
Unknown Probability ◽  
Auto Regression

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.

Feedback Control of Stochastic Systems to Track Prespecified Probability Density Functions

2005 ◽  
Author(s):  
Ozer Elbeyli ◽  
J. Q. Sun
Keyword(s):  
Probability Density ◽  
Stochastic Systems ◽  
Control Design ◽  
Probability Density Functions ◽  
Density Functions ◽  
Moment Equations ◽  
Feedback Controls ◽  
The Moment ◽  
Non Gaussian ◽  
Probability Density Function Pdf

We present a study of feedback controls of stochastic systems to track a prespecified probability density function (PDF). The moment equations of the response are used in the control design to illustrate the underlining issues. A hierarchical approach is proposed to design the control for tracking Gaussian and non-Gaussian PDFs. The control design approach is demonstrated with a simple example.

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