Geodesic
Evolution of moments of isotropic Brownian stochastic flows
Teoriâ slučajnyh processov, Tome 20 (2015) no. 1, pp. 14-27 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2015},
     volume = {20},
     number = {1},
     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
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
%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