Evolution of moments of isotropic Brownian stochastic flows
Teoriâ slučajnyh processov, Tome 20 (2015) no. 1, pp. 14-27.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider the asymptotic behaviour of all moments of the interparticle distance and of all mixed moments of an isotropic Brownian stochastic flow which serves as a smooth approximation of the Arratia flow.
Keywords: Isotropic Brownian stochastic flows, stochastic integral equations, asymptotic behaviour of moments, interparticle distance, Wiener sheet, Arratia flow.
@article{THSP_2015_20_1_a1,
     author = {V. V. Fomichov},
     title = {Evolution of moments of isotropic {Brownian} stochastic flows},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {14--27},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2015_20_1_a1/}
}
TY  - JOUR
AU  - V. V. Fomichov
TI  - Evolution of moments of isotropic Brownian stochastic flows
JO  - Teoriâ slučajnyh processov
PY  - 2015
SP  - 14
EP  - 27
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2015_20_1_a1/
LA  - en
ID  - THSP_2015_20_1_a1
ER  - 
%0 Journal Article
%A V. V. Fomichov
%T Evolution of moments of isotropic Brownian stochastic flows
%J Teoriâ slučajnyh processov
%D 2015
%P 14-27
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2015_20_1_a1/
%G en
%F THSP_2015_20_1_a1
V. V. Fomichov. Evolution of moments of isotropic Brownian stochastic flows. Teoriâ slučajnyh processov, Tome 20 (2015) no. 1, pp. 14-27. http://geodesic.mathdoc.fr/item/THSP_2015_20_1_a1/

[1] D. W. Dean, An analysis of the stochastic approaches to the problems of flow and transport in porous media, Thesis (PhD), University of Colorado at Denver, 1997, 235 pp. | MR

[2] A. A. Dorogovtsev, “One Brownian stochastic flow”, Theory of Stochastic Processes, 10(26):3-4 (2004), 21–25 | MR | Zbl

[3] A. A. Dorogovtsev, Measure-valued processes and stochastic flows, Institute of Mathematics of the NAS of Ukraine, Kiev, 2007, 289 pp. (in Russian) | MR | Zbl

[4] W. Graham, D. McLaughlin, “Stochastic analysis of nonstationary subsurface solute transport: 1. Unconditional moments”, Water Resources Research, 25:2 (1989), 215–232 | DOI

[5] W. Graham, D. McLaughlin, “Stochastic analysis of nonstationary subsurface solute transport: 2. Conditional moments”, Water Resources Research, 25:11 (1989), 2331–2355 | DOI

[6] G. H. Hardy, J. E. Littlewood, G. Pólya, Inequalities, M., 1948, 456 pp. (in Russian)

[7] P. Kotelenez, “A class of quasilinear stochastic partial differential equations of McKean–Vlasov type with mass conservation”, Probability Theory and Related Fields, 102:2 (1995), 159–188 | DOI | MR | Zbl

[8] H. Kunita, Stochastic flows and stochastic differential equations, Cambridge University Press, Cambridge, 1990, 346 pp. | MR | Zbl

[9] Y. Le Jan, “On isotropic Brownian motions”, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 70 (1985), 609–620 | DOI | MR | Zbl

[10] R. S. Liptser, A. N. Shiryaev, Statistics of random processes (non-linear filtering and related topics), Nauka, Moscow, 1974, 696 pp. (in Russian) | MR

[11] H. Matsumoto, “Coalescing stochastic flows on the real line”, Osaka Journal of Mathematics, 26:1 (1989), 139–158 | MR | Zbl

[12] V. Sotiropoulos, Y. Kaznessis, “Analytical derivation of moment equations in stochastic chemical kinetics”, Chemical Engineering Science, 66:3 (2011), 268–277 | DOI

[13] J. B. Walsh, “An introduction to stochastic partial differential equations”, École d'été de probabilités de Saint-Flour XIV–1984, Lecture Notes in Mathematics, 1180, Springer, Berlin – Heidelberg, 1986, 265–439 | DOI | MR

[14] C. L. Zirbel, Stochastic flows: dispersion of a mass distribution and Lagrangian observations of a random field, Dissertation (PhD), Princeton University, 1993, 162 pp. | MR