Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 169-173
Citer cet article
G. L. Kulinič. On the existence and uniqueness of a solution of a stochastic differential equations with martingale differential. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 169-173. http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a15/
@article{TVP_1974_19_1_a15,
author = {G. L. Kulini\v{c}},
title = {On the existence and uniqueness of a~solution of a~stochastic differential equations with martingale differential},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {169--173},
year = {1974},
volume = {19},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a15/}
}
TY - JOUR
AU - G. L. Kulinič
TI - On the existence and uniqueness of a solution of a stochastic differential equations with martingale differential
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1974
SP - 169
EP - 173
VL - 19
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a15/
LA - ru
ID - TVP_1974_19_1_a15
ER -
%0 Journal Article
%A G. L. Kulinič
%T On the existence and uniqueness of a solution of a stochastic differential equations with martingale differential
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1974
%P 169-173
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a15/
%G ru
%F TVP_1974_19_1_a15
Under some conditions, the existence and uniqueness of a solution of the equation $$ d\xi(t)=a(t,\xi(t))dt+\sum_{k=1}^rb_k(t,\xi(t))d\zeta_k(t)+\int_{R^m}f(t,\xi(t),u)\widetilde\nu(dt,du) $$ are proved, where $\zeta_k(t)$, $k=\overline{1,r}$, are continuous martingales, $\widetilde\nu(t,A)=\nu(t,A)-t\Pi(A)$ and $\nu(t,A)$ is a Poisson measure, $\mathbf M\nu(t,A)=t\Pi(A)$.
