DocumentCode :
3686275
Title :
A stochastic density matrix approach to approximation of probability distributions and its application to nonlinear systems
Author :
Igor G. Vladimirov
Author_Institution :
TUNSW Canberra, Australia
fYear :
2015
Firstpage :
1090
Lastpage :
1095
Abstract :
This paper outlines an approach to the approximation of probability density functions by quadratic forms of weighted orthonormal basis functions with positive semi-definite Hermitian matrices of unit trace. Such matrices are called stochastic density matrices in order to reflect an analogy with the quantum mechanical density matrices. The SDM approximation of a PDF satisfies the normalization condition and is nonnegative everywhere in contrast to the truncated Gram-Charlier and Edgeworth expansions. For bases with an algebraic structure, such as the Hermite polynomial and Fourier bases, the SDM approximation can be chosen so as to satisfy given moment specifications and can be optimized using a quadratic proximity criterion. We apply the SDM approach to the Fokker-Planck-Kolmogorov PDF dynamics of Markov diffusion processes governed by nonlinear stochastic differential equations. This leads to an ordinary differential equation for the SDM dynamics of the approximating PDF. As an example, we consider the Smoluchowski SDE on a multidimensional torus.
Keywords :
"Approximation methods","Polynomials","Probability density function","Markov processes","Hilbert space","Zinc","Quantum mechanics"
Publisher :
ieee
Conference_Titel :
Control Applications (CCA), 2015 IEEE Conference on
Type :
conf
DOI :
10.1109/CCA.2015.7320758
Filename :
7320758
Link To Document :
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