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.
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/
@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},
     year = {2014},
     volume = {19},
     number = {1},
     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
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
%U http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a3/
%G en
%F 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[4] Coalescing brownian motion and the voter model on $\mathbb{Z}$, Unpublished partial manuscript, 1981, Available from rarratia@math.usc.edu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