Large deviations principle for finite system of heavy diffusion particles
Teoriâ slučajnyh processov, Tome 19 (2014) no. 1, pp. 37-45.

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

The large deviation principle for a system of coalescing heavy diffusion particles is proved. Some asymptotic properties of the distribution of the first moment of meeting of two particles are described.
Keywords: Large deviation principle, the process of heavy diffusion particles, coalescing particles system.
@article{THSP_2014_19_1_a3,
     author = {V. V. Konarovskyi},
     title = {Large deviations principle for finite system of heavy diffusion particles},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {37--45},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a3/}
}
TY  - JOUR
AU  - V. V. Konarovskyi
TI  - Large deviations principle for finite system of heavy diffusion particles
JO  - Teoriâ slučajnyh processov
PY  - 2014
SP  - 37
EP  - 45
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a3/
LA  - en
ID  - THSP_2014_19_1_a3
ER  - 
%0 Journal Article
%A V. V. Konarovskyi
%T Large deviations principle for finite system of heavy diffusion particles
%J Teoriâ slučajnyh processov
%D 2014
%P 37-45
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a3/
%G en
%F THSP_2014_19_1_a3
V. V. Konarovskyi. Large deviations principle for finite system of heavy diffusion particles. Teoriâ slučajnyh processov, Tome 19 (2014) no. 1, pp. 37-45. http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a3/

[1] V. V. Konarovskiy, “On infinite system of diffusing particles with coalescing”, Theory of Probability and its Applications, 55:1 (2011), 134–144 | DOI | MR

[2] V. V. Konarovskiy, “System of sticking diffusion particles of variable mass”, Ukrainian Mathematical Journal, 62:1 (2010), 97–113 | DOI | MR

[3] R. A. Arratia, Brownian motion on the line, PhD dissertation, Univ. Wiskonsin, Madison, 1979

[4] Coalescing brownian motion and the voter model on $\mathbb{Z}$, Unpublished partial manuscript, 1981, Available from rarratia@math.usc.edu

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

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

[7] V. V. Konarovskii, “The martingale problem for a measure-valued process with heavy diffusion particles”, Theory of Stochastic Processes, 17(33):1 (2011), 50–60 | MR | Zbl

[8] F. Gao, J. Ren, “Large deviations for stochastic flows and their applications”, Science in China Series A: Mathematics, 44:8 (2001), 1016–1033 | DOI | MR | Zbl

[9] A. Budhiraja, P. Dupuis, V. Maroulas, “Large deviations for stochastic flows of diffeomorphisms”, Bernoulli, 16:1 (2010), 234–257 | DOI | MR | Zbl

[10] A. A. Dorogovtsev, O. V. Ostapenko, “Large deviations for flows of interacting Brownian motions”, Stochastics and Dynamics, 10:3 (2010), 315–339 | DOI | MR | Zbl

[11] A. M. Kulik, “Large deviation estimates for solutions of Fredholm-type equations with small random operator perturbations”, Theory of Stochastic Processes, 11(27):1-2 (2011), 81–95 | MR

[12] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, 2nd ed., Springer, New York, 2009 | MR

[13] O. Kallenberg, Foundations of Modern Probability, 2nd ed., Springer, New York, 2002 | MR | Zbl

[14] N. Ikeda, Sh. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland Mathematical Library, Amsterdam, 1981 | MR