Geodesic
Large deviations for one-dimensional SDE with discontinuous diffusion coefficient
Teoriâ slučajnyh processov, Tome 18 (2012) no. 1, pp. 101-110.

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

Large deviation principle is established for a family of solutions to one-dimensional SDE's under the condition that the set of discontinuity points of the diffusion coefficient has zero Lebesgue measure.
Keywords: LDP, one-dimensional SDE, semicontraction principles. 
@article{THSP_2012_18_1_a5,
     author = {Alexei M. Kulik and Daryna D. Soboleva},
     title = {Large deviations for one-dimensional {SDE} with discontinuous diffusion coefficient},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {101--110},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a5/}
}
TY  - JOUR
AU  - Alexei M. Kulik
AU  - Daryna D. Soboleva
TI  - Large deviations for one-dimensional SDE with discontinuous diffusion coefficient
JO  - Teoriâ slučajnyh processov
PY  - 2012
SP  - 101
EP  - 110
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a5/
LA  - en
ID  - THSP_2012_18_1_a5
ER  - 
%0 Journal Article
%A Alexei M. Kulik
%A Daryna D. Soboleva
%T Large deviations for one-dimensional SDE with discontinuous diffusion coefficient
%J Teoriâ slučajnyh processov
%D 2012
%P 101-110
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a5/
%G en
%F THSP_2012_18_1_a5
Alexei M. Kulik; Daryna D. Soboleva. Large deviations for one-dimensional SDE with discontinuous diffusion coefficient. Teoriâ slučajnyh processov, Tome 18 (2012) no. 1, pp. 101-110. http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a5/

[1] M. I. Freidlin, A. D. Wentzell, Random Perturbations of Dynamical Systems, Springer, New York, 1998 | MR | Zbl

[2] T. S. Chiang, S. J. Sheu, “Large deviations of diffusion processes with discontinuous drift and their occupation times”, Ann. Probab., 28 (2000), 140–165 | DOI | MR | Zbl

[3] T. S. Chiang, S. J. Sheu, “Small perturbations of diffusions in inhomogeneous media”, Ann. Inst. Henri Poincaré, 38:3 (2002), 285–318 | DOI | MR | Zbl

[4] I. H. Krykun, “Large deviation principle for stochastic equations with local time”, Theory of Stochastic Processes, 15(31):2 (2009), 140–155 | MR | Zbl

[5] Jin Feng, T. G. Kurtz, Large Deviations for Stochastic Processes, AMS, Providence, RI, 2006 | MR | Zbl

[6] 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 (2005), 81–95 | MR | Zbl

[7] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981 | MR | Zbl

[8] V. I. Bogachev, Differentiable Measures and the Malliavin Calculus, Mathematical Survys and Monographs, 164, AMS, Providence, RI, 2010 | DOI | MR | Zbl

[9] A. N. Kolmogorov, S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover, New York, 1999