Geodesic
Modeling evolution sample distributions of random quantities by the equation of Liuville
Matematičeskoe modelirovanie, Tome 32 (2020) no. 1, pp. 111-128

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The difference approximation of the one-dimensional Liouville equation for the sample distribution density of the non-stationary time series estimated by the histogram is considered. We prove a necessary and sufficient condition that the change in the sample density of the distribution over a certain period of time can be modeled as the evolution of the density according to the Liouville equation. This condition is a strong positivity of the initial density distribution in the inner class intervals. The determination of the corresponding velocity algorithm is constructed and its mechanical-statistical meaning is shown as a semigroup equivalent in Chernoff sense to the average semigroup, generating the evolution of the distribution function.
Mots-clés : Liouville equation
Keywords: non-stationary time series, sample distribution function, Chernoff equivalence. 
@article{MM_2020_32_1_a7,
     author = {A. A. Kislitsin and Yu. N. Orlov},
     title = {Modeling evolution sample distributions of random quantities by the equation of {Liuville}},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {111--128},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_1_a7/}
}
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A. A. Kislitsin; Yu. N. Orlov. Modeling evolution sample distributions of random quantities by the equation of Liuville. Matematičeskoe modelirovanie, Tome 32 (2020) no. 1, pp. 111-128. http://geodesic.mathdoc.fr/item/MM_2020_32_1_a7/