Geodesic
On a class of boundary-value problems for stochastic differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 43 (1980) no. 2, pp. 240-252 
S. E. Pitovranov; V. M. Chetverikov. On a class of boundary-value problems for stochastic differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 43 (1980) no. 2, pp. 240-252. http://geodesic.mathdoc.fr/item/TMF_1980_43_2_a6/
@article{TMF_1980_43_2_a6,
     author = {S. E. Pitovranov and V. M. Chetverikov},
     title = {On~a~class of~boundary-value problems for stochastic differential equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {240--252},
     year = {1980},
     volume = {43},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_43_2_a6/}
}
TY  - JOUR
AU  - S. E. Pitovranov
AU  - V. M. Chetverikov
TI  - On a class of boundary-value problems for stochastic differential equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1980
SP  - 240
EP  - 252
VL  - 43
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1980_43_2_a6/
LA  - ru
ID  - TMF_1980_43_2_a6
ER  - 
%0 Journal Article
%A S. E. Pitovranov
%A V. M. Chetverikov
%T On a class of boundary-value problems for stochastic differential equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1980
%P 240-252
%V 43
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1980_43_2_a6/
%G ru
%F TMF_1980_43_2_a6

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

Boundary value problems of general kind for a system of ordinary stochastic differential equations are considered. The $q$-time density of probability is built in the case when the boundary value problem possesses the unique solution or countable set of solutions. Some concrete computational examples are considered to illustrate the scheme. Several uniqueness theorems for the initial boundary value problem are proved.

[1] I. I. Gikhman, A. V. Skorokhod, Vvedenie v teoriyu sluchainykh protsessov, «Nauka», 1977 | MR

[2] R. L. Stratonovich, Izbrannye voprosy teorii fluktuatsii v radiotekhnike, «Sov. radio», 1961 ; Условные марковские процессы и их применение к теории оптимального управления, МГУ, 1966 | Zbl

[3] V. I. Klyatskin, V. I. Tatarskii, TMF, 17 (1973), 273

[4] V. I. Klyatskin, Statisticheskoe opisanie dinamicheskikh sistem s fluktuiruyuschimi parametrami, «Nauka», 1975

[5] S. E. Pitovranov, V. M. Chetverikov, TMF, 35 (1978), 211 | MR | Zbl

[6] V. I. Klyatskin, Izv. VUZov, radiofizika, 20 (1977), 1165

[7] A. I. Saichev, Izv. VUZov, radiofizika, 21 (1978), 996

[8] V. I. Klyatskin, Izv. VUZov, radiofizika, 20 (1977), 1752

[9] Dzh. Kasti, R. Kalaba, Metody pogruzheniya v prikladnoi matematike, «Mir», 1976 | MR

[10] M. Golberg, Appl. Math. Comput., 1 (1975), 1 | DOI | MR

[11] V. P. Maslov, Teoriya vozmuschenii i asimptoticheskie metody, MGU, 1965 ; Операторные методы, «Наука», 1973 | MR | MR

[12] V. M. Chetverikov, TMF, 23 (1975), 383

[13] F. Khartman, Obyknovennye differentsialnye uravneniya, «Mir», 1970 | MR | Zbl