Geodesic
Estimates for overshooting an arbitrary boundary by a random walk and their applications
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 2, pp. 249-277 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Estimates are found for the magnitude of overshoot, by a sequence of random variables, over an arbitrary boundary. If the sequence increments satisfy a so-called condition of asymptotic homogeneity and the boundary is asymptotically “smooth” then the occurrence of the weak convergence to a limit shape (as the boundary is sent away) is established for the distribution of the overshoot value. As an application, we obtain a uniform (over the class of distributions) basic renewal theorem and determine the asymptotics of the average time of crossing a curvilinear border by the trajectories of asymptotically homogeneous Markov chains.
Keywords: sequence of random variables, random walk, time and value of the first overshoot, uniform integrability, nonlinear boundary, asymptotic homogeneity.
Mots-clés : Markov chain 
@article{TVP_1999_44_2_a1,
     author = {A. A. Borovkov and S. G. Foss},
     title = {Estimates for overshooting an arbitrary boundary by a random walk and their applications},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {249--277},
     year = {1999},
     volume = {44},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_2_a1/}
}
TY  - JOUR
AU  - A. A. Borovkov
AU  - S. G. Foss
TI  - Estimates for overshooting an arbitrary boundary by a random walk and their applications
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1999
SP  - 249
EP  - 277
VL  - 44
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_1999_44_2_a1/
LA  - ru
ID  - TVP_1999_44_2_a1
ER  - 
%0 Journal Article
%A A. A. Borovkov
%A S. G. Foss
%T Estimates for overshooting an arbitrary boundary by a random walk and their applications
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1999
%P 249-277
%V 44
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1999_44_2_a1/
%G ru
%F TVP_1999_44_2_a1
A. A. Borovkov; S. G. Foss. Estimates for overshooting an arbitrary boundary by a random walk and their applications. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 2, pp. 249-277. http://geodesic.mathdoc.fr/item/TVP_1999_44_2_a1/