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SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2018, Volume 56, Issue 1, pp. 570 - 589
We develop a finite-dimensional approximation of the Frobenius-Perron operator using the finite volume method applied to the continuity equation for the... 
Sequential inference | Finite volume method | Frobenius–Perron operator | Markov operator | MATHEMATICS, APPLIED | sequential inference | ERROR ESTIMATE | finite volume method | Frobenius-Perron operator
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 07/2018, Volume 28, Issue 7, p. 075309
A basic systems question concerns the concept of closure, meaning autonomy (closed) in the sense of describing the (sub)system as fully consistent within... 
CHAOS | MATHEMATICS, APPLIED | INVARIANT-MEASURES | DYNAMICAL-SYSTEMS | OPTIMAL CAUSATION ENTROPY | DIVERGENCE | ULAMS METHOD | FINITE APPROXIMATIONS | PHYSICS, MATHEMATICAL | FROBENIUS-PERRON OPERATOR | TRANSFORMATIONS | CONJECTURE
Journal Article
Neural Networks, ISSN 0893-6080, 08/2013, Volume 44, pp. 1 - 5
The goal of the article is to establish the contractivity, on the space of normalised positive distributions, of a certain class of Markov operators defined by... 
Stationary densities | Learning algorithms | Stochastic approximation | Frobenius–Perron operator | Artificial neural networks | Convergence | Frobenius-Perron operator | STOCHASTIC ALGORITHMS | NEUROSCIENCES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Time Factors | Markov Chains | Neural Networks (Computer) | Algorithms
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 10/2012, Volume 219, Issue 3, pp. 1047 - 1052
Let S:[0,1]→[0,1] be a nonsingular transformation such that the corresponding Frobenius–Perron operator PS:L1(0,1)→L1(0,1) has a stationary density f∗. We... 
Pulse function | Frobenius–Perron operator | Stationary density | Ulam’s method | Delta function | Ulam's method | Frobenius-Perron operator | MATHEMATICS, APPLIED | INVARIANT-MEASURES | ULAMS CONJECTURE
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 01/2017, Volume 328, pp. 95 - 108
Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave... 
High frequency asymptotics | Ray tracing | Geometrical optics/acoustics | Frobenius–Perron operator | Vibro-acoustics | Statistical energy analysis | DYNAMICAL ENERGY ANALYSIS | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Frobenius-Perron operator | PHYSICS, MATHEMATICAL
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2010, Volume 217, Issue 7, pp. 3257 - 3262
We propose a piecewise linear numerical method based on least squares approximations for computing stationary density functions of Frobenius–Perron operators... 
Absolutely continuous invariant measures | Least squares | Frobenius–Perron operators | Frobenius-Perron operators | MATHEMATICS, APPLIED | ULAMS METHOD | Operators | Approximation | Computation | Least squares method | Norms | Mathematical models | Density | Convergence
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2012, Volume 386, Issue 1, pp. 91 - 102
In this paper we prove both the L 1 -norm and the BV-norm convergence for a piecewise linear least squares approximation method that was recently proposed for... 
Invariant measures | Least squares approximations | Frobenius–Perron operators | Frobenius-Perron operators | FINITE APPROXIMATION | MATHEMATICS | MATHEMATICS, APPLIED | MAPS | ULAMS METHOD
Journal Article
Indian Journal of Pure and Applied Mathematics, ISSN 0019-5588, 6/2012, Volume 43, Issue 3, pp. 263 - 278
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2006, Volume 182, Issue 1, pp. 210 - 212
Let T be a non-singular transformation on [0, 1]. We give conditions which ensure convergence of a method of Ding for approximating T-invariant measures. In... 
Invariant measure | Maximum entropy | Frobenius–Perron operator | Frobenius-Perron operator | maximum entropy | MATHEMATICS, APPLIED | invariant measure
Journal Article
New Journal of Physics, ISSN 1367-2630, 01/2016, Volume 18, Issue 1, p. 15005
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2015, Volume 421, Issue 2, pp. 1487 - 1501
Let the Frobenius-Perron operator P :L (0, 1)→L (0, 1), related to a nonsingular transformation S:[0, 1]→[0, 1], have an invariant density f*. We propose a... 
Partition of unity | Invariant density | Maximum entropy | Frobenius-Perron operator | Nonsingular transformation | MATHEMATICS | MATHEMATICS, APPLIED | FROBENIUS-PERRON OPERATORS | Analysis | Methods | Algorithms
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 11/2018, Volume 28, Issue 12, p. 1850154
We present a numerical method for the approximation of absolutely continuous invariant measures of one-dimensional random maps, based on the maximum entropy... 
invariant measures | Maximum entropy principle | random maps | Markov operators | INTERVAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | STATIONARY DENSITY | MULTIDISCIPLINARY SCIENCES | FROBENIUS-PERRON OPERATOR
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 09/2012, Volume 38, Issue 3, pp. 817 - 826
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2007, Volume 67, Issue 3, pp. 763 - 772
We present lower and upper error bounds under the BV-norm for piecewise linear Markov finite approximations to Frobenius–Perron operators in terms of the... 
Markov approximation | Error estimates | Frobenius–Perron operator | Invariant measure | Frobenius-Perron operator | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUOUS INVARIANT-MEASURES | ULAMS CONJECTURE | invariant measure | FINITE APPROXIMATIONS | error estimates | TRANSFORMATIONS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2019, Volume 479, Issue 1, pp. 337 - 349
Using matrix norm techniques, we give a unified convergence analysis of a general projection method for computing stationary density functions of... 
Projection | Matrix norm | Invariant measure | Frobenius-Perron operator | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANT-MEASURES | PIECEWISE | APPROXIMATIONS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2006, Volume 174, Issue 1, pp. 236 - 251
In this paper, we propose a modified piecewise linear Markov method for approximating Markov operators defined on L 1(0, 1). We present numerical results with... 
Markov finite approximations | Markov operators | MATHEMATICS, APPLIED | FINITE APPROXIMATIONS | TRANSFORMATIONS | FROBENIUS-PERRON OPERATORS
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 11/2009, Volume 35, Issue 2, pp. 85 - 96
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2002, Volume 147, Issue 1, pp. 137 - 152
In this paper we survey some recent developments in the numerical analysis of Markov operators, and in particular Frobenius–Perron operators associated with... 
Frobenius-Perron operators | Finite approximations | Invariant measures | Markov operators | invariant measures | MATHEMATICS, APPLIED | MULTIDIMENSIONAL TRANSFORMATIONS | MAPS | CONTINUOUS INVARIANT-MEASURES | STABILITY | finite approximations | ULAMS METHOD | CONJECTURE
Journal Article
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