Geodesic
Statistical structuring theory in parametrically excitable dynamical systems with a~Gaussian pump
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 3, pp. 475-495

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Based on the idea of the statistical topography, we analyze the problem of emergence of stochastic structure formation in linear and quasilinear problems described by first-order partial differential equations. The appearance of a parametric excitation on the background of a Gaussian pump is a specific feature of these problems. We obtain equations for the probability density of the solutions of these equations, whence it follows that the stochastic structure formation emerges with probability one, i.e., for almost every realization of the random parameters of the medium.
Mots-clés : Liouville equation, diffusion approximation
Keywords: probability density, integral probability distribution function, typical realization curve, statistical topography, clustering. 
@article{TMF_2016_186_3_a8,
     author = {V. I. Klyatskin and K. V. Koshel'},
     title = {Statistical structuring theory in parametrically excitable dynamical systems with {a~Gaussian} pump},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {475--495},
     publisher = {mathdoc},
     volume = {186},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_3_a8/}
}
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V. I. Klyatskin; K. V. Koshel'. Statistical structuring theory in parametrically excitable dynamical systems with a~Gaussian pump. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 3, pp. 475-495. http://geodesic.mathdoc.fr/item/TMF_2016_186_3_a8/