Research paperA matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems

- 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.
- The main assumption is that the one-dimensional transformation that generated the densities is piecewise-linear, semi-Markov.
- A matrix approximation of the transfer operator associated with the stochastically perturbed transformation, which forms the basis for the reconstruction algorithm, is introduced.
- 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.
- The algorithm is extended to nonlinear continuous maps.
- 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.