Geodesic
Weak convergence of a series scheme of Markov chains to the solution of a L\'evy driven SDE
Teoriâ slučajnyh processov, Tome 18 (2012) no. 1, pp. 86-100.

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

Under the assumptions analogous to those of Gnedenko's theorem, the weak convergence of a series scheme of Markov chains to the solution of a Lévy driven SDE is obtained.
Keywords: Lévy driven SDE, weak convergence of Markov chains. 
@article{THSP_2012_18_1_a4,
     author = {T. I. Kosenkova},
     title = {Weak convergence of a series scheme of {Markov} chains to the solution of a {L\'evy} driven {SDE}},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {86--100},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a4/}
}
TY  - JOUR
AU  - T. I. Kosenkova
TI  - Weak convergence of a series scheme of Markov chains to the solution of a L\'evy driven SDE
JO  - Teoriâ slučajnyh processov
PY  - 2012
SP  - 86
EP  - 100
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a4/
LA  - en
ID  - THSP_2012_18_1_a4
ER  - 
%0 Journal Article
%A T. I. Kosenkova
%T Weak convergence of a series scheme of Markov chains to the solution of a L\'evy driven SDE
%J Teoriâ slučajnyh processov
%D 2012
%P 86-100
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a4/
%G en
%F THSP_2012_18_1_a4
T. I. Kosenkova. Weak convergence of a series scheme of Markov chains to the solution of a L\'evy driven SDE. Teoriâ slučajnyh processov, Tome 18 (2012) no. 1, pp. 86-100. http://geodesic.mathdoc.fr/item/THSP_2012_18_1_a4/

[1] I. I. Gikhman, A. V. Skorokhod, Introduction to the Theory of Stochastic Processes, Dover, New York, 1996 | MR

[2] B. V. Gnedenko, A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, MA, 1954 | MR | Zbl

[3] I. I. Gikhman, A. V. Skorokhod, Stochastic Diffential Equations and Their Applications, Springer, Berlin, 1972

[4] V. S. Koroliuk, N. Limnios, I. V. Samoilenko, “Lévy approximation of impulsive recurrent process with semi-Markov switching”, Theory of Probability and Mathematical Statistics, 2009, no. 80, 85–92 | MR

[5] R. F. Bass, “Uniqueness in law for pure jump Markov processes”, Probab. Th. Rel. Fields, 1988, no. 79, 271–287 | DOI | MR | Zbl

[6] S. N. Ethier, T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986 | MR | Zbl