Geodesic
On the Absolute Continuity of Measures Corresponding to Diffusion Type Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 1, pp. 173-178 
M. P. Ershov. On the Absolute Continuity of Measures Corresponding to Diffusion Type Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 1, pp. 173-178. http://geodesic.mathdoc.fr/item/TVP_1972_17_1_a16/
@article{TVP_1972_17_1_a16,
     author = {M. P. Ershov},
     title = {On the {Absolute} {Continuity} of {Measures} {Corresponding} to {Diffusion} {Type} {Processes}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {173--178},
     year = {1972},
     volume = {17},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_1_a16/}
}
TY  - JOUR
AU  - M. P. Ershov
TI  - On the Absolute Continuity of Measures Corresponding to Diffusion Type Processes
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1972
SP  - 173
EP  - 178
VL  - 17
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TVP_1972_17_1_a16/
LA  - ru
ID  - TVP_1972_17_1_a16
ER  - 
%0 Journal Article
%A M. P. Ershov
%T On the Absolute Continuity of Measures Corresponding to Diffusion Type Processes
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1972
%P 173-178
%V 17
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1972_17_1_a16/
%G ru
%F TVP_1972_17_1_a16

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

In the paper, conditions are studied under which the measures corresponding to Wiener processes with different drifts are equivalent. The main theorem assepts that, if the drift coefficient (measurable with respect to the past of the observation process) is square integrable a.s. at both «observation-process» and «Wiener-process point», then the measures of the process are equivalent. The result is applied to the existence and uniqueness of a weak of the stochastic equation $d\xi=\gamma(t,\xi)\,dt+dW$.