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A Survey Of The Methods To Find Probability Density Functions, Nancy Picinic Ricca
A Survey Of The Methods To Find Probability Density Functions, Nancy Picinic Ricca
Theses, Dissertations and Culminating Projects
Various methods are described in this thesis that will approximate probability density functions (PDF), also known as invariant measures for chaotic maps. When studying discrete dynamical systems, the measure of a map is important in describing its behavior because it captures the statistics of long term simulations. Being invariant means that this distribution remains the same, no matter when you observe it. The main goal is to understand how to obtain these PDFs for various one-dimensional maps using alternative methods to time series data.
The methods studied in this thesis include the Z-matrix and the Frobenius-Perron Operator, which are analytic …