Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5011375 | Communications in Nonlinear Science and Numerical Simulation | 2018 | 19 Pages |
â¢The paper introduces new method of reconstructing an unknown one-dimensional transformation that is subject to constantly applied stochastic perturbations based on temporal sequences of probability density functions.â¢The main assumption is that the one-dimensional transformation that generated the densities is piecewise-linear, semi-Markov.â¢A matrix approximation of the transfer operator associated with the stochastically perturbed transformation, which forms the basis for the reconstruction algorithm, is introduced.â¢A practical algorithm to estimate the matrix-representation of the Frobenius-Perron operator associated with the unperturbed transformation and reconstruct the onedimensional map is proposed.â¢The algorithm is extended to nonlinear continuous maps.â¢Numerical simulation examples are provided to demonstrate the performance of the approach and to compare it with that of an existing algorithm.
The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.