Parametric probability density estimation based on an approximation by a discretized stochastic differential equation

Author

Vesin, J.M. ; Kunt, M.

Author_Institution

Lab. de Traitement des Signaux, Ecole Polytech. Federale de Lausanne, Switzerland

fYear

1991

fDate

14-17 Apr 1991

Firstpage

2061

Abstract

The authors present a parametric probability density estimation technique for Markov processes defined by a first-order nonlinear autoregressive equation. It is based on the approximation of these processes as sampled versions of the continuous-time solutions of stochastic differential equations (SDEs) via the discretization scheme presented by T. Ozaki (1985). First, a polynomial estimate of the nonlinear recursion function is obtained from the data and then a suitable transformation of its coefficients is performed in order to obtain an estimate of the function in the corresponding SDE. The PDF estimate is then the equilibrium PDF of this SDE

Keywords

Markov processes; differential equations; polynomials; signal processing; statistical analysis; Markov processes; continuous-time solutions; discretized stochastic differential equation; equilibrium PDF; first-order nonlinear autoregressive equation; nonlinear recursion function; parametric probability density estimation; polynomial estimate; signal processing; Differential equations; Markov processes; Nonlinear equations; Pattern recognition; Polynomials; Probability density function; Recursive estimation; Stochastic processes; Stochastic resonance; White noise;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference on

Conference_Location

Toronto, Ont.

ISSN

1520-6149

Print_ISBN

0-7803-0003-3

Type

conf

DOI

10.1109/ICASSP.1991.150810

Filename

150810