Geodesic
Stochastic differential equations with interaction and the law of iterated logarithm
Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 54-58.

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

We consider a one-dimensional stochastic differential equation with interaction with no drift part. For single trajectories, we obtain the result similar to the law of iterated logarithm for a Wiener process.
Keywords: Law of iterated logarithm, stochastic flow, stochastic differential equation with interaction, measure-valued process. 
@article{THSP_2012_18_2_a5,
     author = {M. P. Lagunova},
     title = {Stochastic differential equations with interaction and the law of iterated logarithm},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {54--58},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a5/}
}
TY  - JOUR
AU  - M. P. Lagunova
TI  - Stochastic differential equations with interaction and the law of iterated logarithm
JO  - Teoriâ slučajnyh processov
PY  - 2012
SP  - 54
EP  - 58
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a5/
LA  - en
ID  - THSP_2012_18_2_a5
ER  - 
%0 Journal Article
%A M. P. Lagunova
%T Stochastic differential equations with interaction and the law of iterated logarithm
%J Teoriâ slučajnyh processov
%D 2012
%P 54-58
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a5/
%G en
%F THSP_2012_18_2_a5
M. P. Lagunova. Stochastic differential equations with interaction and the law of iterated logarithm. Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 54-58. http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a5/

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

[2] G. L. Kulinič, “On the law of iterated logarithm for one-dimensional diffusion processes”, Teor. Veroyat. Primen., 29 (1984), 544–547 | MR | Zbl

[3] L. Caramellino, “Strassen's law of the iterated logarithm for diffusion processes for small time”, Stoch. Process. Their Appl., 74 (1998), 1-19 | DOI | MR | Zbl

[4] O. Kallenberg, Foundations of Modern Probability, Springer, Berlin, 2002 | MR | Zbl

[5] M. P. Karlikova, “On a weak solution of an equation for an evolutionary flow with interaction”, Ukr. Math. J., 57:7 (2005), 1055–1065 | DOI | MR | Zbl

[6] S. H. Strogatz, “From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Bifurcations, patterns and symmetry”, Phys. D, 143:1-4 (2000), 1-20 | DOI | MR | Zbl