Geodesic
A limit theorem for the number of sign changes for a
Teoriâ slučajnyh processov, Tome 14 (2008) no. 2, pp. 79-92.

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

@article{THSP_2008_14_2_a9,
     author = {Alexey M. Kulik},
     title = {A limit theorem for the number of sign changes for a},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {79--92},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2008_14_2_a9/}
}
TY  - JOUR
AU  - Alexey M. Kulik
TI  - A limit theorem for the number of sign changes for a
JO  - Teoriâ slučajnyh processov
PY  - 2008
SP  - 79
EP  - 92
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2008_14_2_a9/
LA  - en
ID  - THSP_2008_14_2_a9
ER  - 
%0 Journal Article
%A Alexey M. Kulik
%T A limit theorem for the number of sign changes for a
%J Teoriâ slučajnyh processov
%D 2008
%P 79-92
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2008_14_2_a9/
%G en
%F THSP_2008_14_2_a9
Alexey M. Kulik. A limit theorem for the number of sign changes for a. Teoriâ slučajnyh processov, Tome 14 (2008) no. 2, pp. 79-92. http://geodesic.mathdoc.fr/item/THSP_2008_14_2_a9/

[1] I. I. Gikhman, “Some limit theorems for the number of intersections of the boundary of a domain by a random function”, Sci. Notes of Kiev Univ., 16:10 (1957), 149-–164 (in Ukrainian) | MR

[2] I. I. Gikhman, “Asymptotic distributions for the number of intersections of the boundary of a domain by a random function”, Visnyk Kiev Univ., Ser. Astronomy, Mathematics and Mechanics, 1:1 (1958), 25-–46 (in Ukrainian) | MR

[3] N. I. Portenko, “The development of I.I.Gikhman’s idea concerning the methods for investigating local behavior of diffusion processes and their weakly convergent sequences”, Theor. Probability and Math. Statist., 50 (1994), 7-–22 | MR | Zbl

[4] H. Al Farah, M. I. Portenko, Limit theorem for the number of intersections of the fixed level by weakly convergent sequence of diffusion processes, Preprint 2007.6, Institute of Math., Kiev, 24, 2007 (in Ukrainian)

[5] arXiv: 0704.0508v1

[6] I. I. Gikhman, A. V. Skorokhod, Stochastic Differential Equations and Their Applications, 2-nd ed, Nauk. Dumka, Kiev, 1982 (in Russian) | MR | Zbl

[7] E. B. Dynkin, Markov Processes, Moscow, 1963 (in Russian) | MR

[8] A. M. Kulik, “Markov approximation of stable processes by random walks”, Theory of Stochastic Processes, 12(28):1-2 (2006), 87-–93 | MR | Zbl

[9] J. L. Doob, Stochastic Processes, Wiley, NY, 1953 | MR | Zbl

[10] A. M. Kulik, “The optimal coupling property and its applications: limit theorems for non-elliptic diffusions and construction of canonical stochastic flow”, Theory of Stochastic Processes, 9(25):1-2 (2003), 82-–98 | MR | Zbl

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

[12] O. F. Porper, S. D. Eidelman, “Asymptotic behavior of the classical and generalized one-dimensional parabolic equations of second order”, Trudy Mosk. Mat. Ob., 36, Mosc. Univ., 1978, 85-–130 (in Russian) | MR | Zbl

[13] S. Nakao, “On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations”, Osaka J. Math, 9 (1972), 513-–518 | MR | Zbl

[14] J. M. Harrison, L. A. Shepp, “On skew Brownian motion”, Annals of Probability, 9:2 (1981), 309-–313 | DOI | MR | Zbl