Geodesic
Asymptotic behavior of solutions to stochastic differential equations with interaction
Teoriâ slučajnyh processov, Tome 25 (2020) no. 2, pp. 1-8.

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

Two-dimensional stochastic differential equation with interaction is considered. The large time behavior of the distance between two solutions starting from different points is studied. A nonzero limit that characterize this distance together with the analogue of the triangle inequality for the map that characterize the limit distance are obtained.
Keywords: SDE with interaction, distance between solutions, long time behavior of solutions. 
@article{THSP_2020_25_2_a0,
     author = {M. A. Belozerova},
     title = {Asymptotic behavior of solutions to stochastic differential equations with interaction},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {1--8},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a0/}
}
TY  - JOUR
AU  - M. A. Belozerova
TI  - Asymptotic behavior of solutions to stochastic differential equations with interaction
JO  - Teoriâ slučajnyh processov
PY  - 2020
SP  - 1
EP  - 8
VL  - 25
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a0/
LA  - en
ID  - THSP_2020_25_2_a0
ER  - 
%0 Journal Article
%A M. A. Belozerova
%T Asymptotic behavior of solutions to stochastic differential equations with interaction
%J Teoriâ slučajnyh processov
%D 2020
%P 1-8
%V 25
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a0/
%G en
%F THSP_2020_25_2_a0
M. A. Belozerova. Asymptotic behavior of solutions to stochastic differential equations with interaction. Teoriâ slučajnyh processov, Tome 25 (2020) no. 2, pp. 1-8. http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a0/

[1] Peter Baxendale, Theodore E. Harris, “Isotropic Stochastic Flows”, Ann. Probab., 14:4 (1986), 1155–1179

[2] M. Cranston, Y. Le Jan, “Geometric evolution under isotropic stochastic flow”, Electronic journal of probability, 3:4 (1998), 1–36

[3] M. Cranston, Y. Le Jan, “A Central Limit Theorem for isotropic flows”, Stochastic Processes and their Applications, 119 (2009), 3767–3784

[4] G. Dimitroff, M. Scheutzow, “Dispersion of volume under the action of isitropic Brownian flows”, Stochastic Processes and their Applications, 119:2, 588–601

[5] A. A. Dorogovtsev, “Stochastic flows with interactions and measure-valued processes”, International Journal of Mathematics and Mathematical Sciences, 63 (2003), 3963–3977

[6] A. A. Dorogovtsev, “Measure-valued Markov processes and stochastic flows on abstract spaces”, Stoch. Rep., 76:5 (2004), 395–407

[7] A. A. Dorogovtsev, Measure-valued processes and stochastic flows, Proceedings of Institute of Mathematics of NAS of Ukraine. Mathematics and its Applications, Kyiv, 2007 (Russian)

[8] Andrey A. Dorogovtsev, Maria P. Karlikova, “Long-time behaviour of measure-valued processes correspondent to stochastic flows with interaction”, Theory of stochastic processes, 9 (25):1–2 (2003), 52–59

[9] N. Ikeda, S. Watanabe, “Stochastic flows of diffeomorphisms”, Stochastic analysis and Applications, Dekker, New York, 179–198

[10] Yves Le Jan, “On isotropic Brownian Motions”, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 70 (1985), 609–620

[11] O. Kallenberg, Foundations of Modern Probability, 2nd ed., Springer. Series in Statistics, 2002

[12] H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, 1990, 361 pp.

[13] M. P. Lagunova, “Stochastic differential equations with interaction and the law of iterated logarithm”, Theory of Stochastic Processes, 18(34) \year 2012:2, 54–58

[14] Ya. B. Zel'dovich, S. A. Molchanov, A. A. Ruzmaikin, D. D. Sokolov, “Intremittency in random media”, Usp. Fiz. Nauk, 152 (1987), 3–32

[15] Craig L. Zirbel, Random measures carried by Brownian flows on $R^d$, Bowling Green State University, 1995

[16] Craig L. Zirbel, Erhan Çinlar, “Mass transport by Brownian flows”, Stochastic Models in Geosystems. The IMA Volumes in Mathematics and its Applications, 85 (1997), 459–492

[17] Craig L.Zirbel, Erhan Çinlar, “Dispersion of Particle Systems in Brownian Flows”, Advances in Applied Probability, 28:1 (1996), 53–74

[18] Craig L. Zirbel, “Translation and dispersion of mass by isotropic brownian flows”, Stochastic Processes and their Applications, 70:1 (1997), 1–29