Geodesic
On the selection of a~Markov process from a~system of processes and the construction of quasi-diffusion processes
Izvestiya. Mathematics , Tome 7 (1973) no. 3, pp. 691-709.

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

In this paper the notion of a Markov system of processes is introduced, and it is proved that a Markov process can be selected from such a system. The usefulness of this fact is illustrated by the example of constructing quasidiffusion processes with “poor” coefficients (e.g. with a degenerate diffusion matrix). 
@article{IM2_1973_7_3_a12,
     author = {N. V. Krylov},
     title = {On the selection of {a~Markov} process from a~system of processes and the construction of quasi-diffusion processes},
     journal = {Izvestiya. Mathematics },
     pages = {691--709},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a12/}
}
TY  - JOUR
AU  - N. V. Krylov
TI  - On the selection of a~Markov process from a~system of processes and the construction of quasi-diffusion processes
JO  - Izvestiya. Mathematics 
PY  - 1973
SP  - 691
EP  - 709
VL  - 7
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a12/
LA  - en
ID  - IM2_1973_7_3_a12
ER  - 
%0 Journal Article
%A N. V. Krylov
%T On the selection of a~Markov process from a~system of processes and the construction of quasi-diffusion processes
%J Izvestiya. Mathematics 
%D 1973
%P 691-709
%V 7
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a12/
%G en
%F IM2_1973_7_3_a12
N. V. Krylov. On the selection of a~Markov process from a~system of processes and the construction of quasi-diffusion processes. Izvestiya. Mathematics , Tome 7 (1973) no. 3, pp. 691-709. http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a12/

[1] Girsanov I. V., “Primer needinstvennosti resheniya stokhasticheskogo uravneniya K. Ito”, Teoriya veroyatn. i ee primen., VII:3 (1962), 336–342

[2] Dynkin E. B., Markovskie protsessy, Fizmatgiz, M., 1963 | MR

[3] Stroock D. W., Varadhan S. R. S., “Diffusion processes with continuous coefficients, I”, Comm. Pure Appl. Math., 22:3 (1969), 346–400 | DOI | MR

[4] Krylov N. V., “O regulyarnosti uslovnykh veroyatnostei dlya sluchainykh protsessov”, Teoriya veroyatn. i ee primen., 18:1 (1973), 151–155 | MR | Zbl

[5] Krylov N. V., “Ob upravlenii resheniem stokhasticheskogo integralnogo uravneniya”, Teoriya veroyatn. i ee primen., 17:1 (1972), 111–127 | MR

[6] Skorokhod A. V., Issledovaniya po teorii sluchainykh protsessov, Kievsk. un-t, Kiev, 1961 | Zbl

[7] Krylov N. V., “O stokhasticheskikh integralnykh uravneniyakh Ito”, Teoriya veroyatn. i ee primen., XIV:2 (1969), 340–348 | MR

[8] Prokhorov Yu. V., “Skhodimost sluchainykh protsessov i predelnye teoremy teorii veroyatnostei”, Teoriya veroyatn. i ee primen., 1:2 (1956), 177–238 | MR

[9] Bekkenbakh E., Bellman R., Neravenstva, Mir, M., 1965 | MR

[10] Krylov N. V., “Diffuziya na ploskosti s otrazheniem. Postroenie protsessa”, Sibirsk. matem. zh., 10:2 (1969), 343–354 | MR | Zbl

[11] Shiryaev A. N., Statisticheskii posledovatelnyi analiz, Nauka, M., 1969 | MR