Geodesic
Dynamic reconstruction of disturbances in stochastic differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1806-1815 
V. L. Rozenberg. Dynamic reconstruction of disturbances in stochastic differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1806-1815. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a5/
@article{ZVMMF_2011_51_10_a5,
     author = {V. L. Rozenberg},
     title = {Dynamic reconstruction of disturbances in stochastic differential equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1806--1815},
     year = {2011},
     volume = {51},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a5/}
}
TY  - JOUR
AU  - V. L. Rozenberg
TI  - Dynamic reconstruction of disturbances in stochastic differential equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1806
EP  - 1815
VL  - 51
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a5/
LA  - ru
ID  - ZVMMF_2011_51_10_a5
ER  - 
%0 Journal Article
%A V. L. Rozenberg
%T Dynamic reconstruction of disturbances in stochastic differential equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1806-1815
%V 51
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a5/
%G ru
%F ZVMMF_2011_51_10_a5

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

The reconstruction of the unknown deterministic disturbance in an Ito stochastic differential equation is studied using the Osipov–Kryazhimskii dynamic inversion theory. Inexact discrete observations of the current phase state are used as input data. A finite-step solving algorithm based on the method of auxiliary controllable models is proposed. Its convergence is proved, and the compatibility conditions for the parameters are given.

[1] Kryazhimskii A. V., Osipov Yu. S., “O modelirovanii upravleniya v dinamicheskoi sisteme”, Izv. AN SSSR. Tekhn. kibernetika, 1983, no. 2, 51–60 | MR

[2] Osipov Yu. S., Vasilev F. P., Potapov M. M., Osnovy metoda dinamicheskoi regulyarizatsii, MGU, M., 1999

[3] Osipov Yu. S., Kryazhimski A. V., Inverse problems for ordinary differential equations: dynamical solutions, Gordon and Breach, London, 1995 | MR | Zbl

[4] Maksimov V. I., Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem, UrO RAN, Ekaterinburg, 2000

[5] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1984 | MR

[6] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1978 | Zbl

[7] Osipov Yu. S., Kryazhimskii A. V., “Pozitsionnoe modelirovanie stokhasticheskogo upravleniya v dinamicheskikh sistemakh”, Dokl. Mezhdunar. konf. po stokhastich. optimizatsii (Kiev, 9–16 sentyabrya, 1984), 43–45

[8] Shiryaev A. N., Veroyatnost, statistika, sluchainye protsessy, MGU, M., 1974

[9] Oksendal V., Stokhasticheskie differentsialnye uravneniya. Vvedenie v teoriyu i prilozheniya, Mir, M., 2003

[10] Pugachev B. C., Sinitsyn I. N., Stokhasticheskie differentsialnye sistemy, Nauka, M., 1985 | MR | Zbl

[11] Rozenberg V. L., “Zadacha dinamicheskogo vosstanovleniya neizvestnoi funktsii v lineinom stokhasticheskom differentsialnom uravnenii”, Avtomatika i telemekhan., 2007, no. 11, 76–87 | MR | Zbl

[12] Krasovskii N. N., Kotelnikov A. N., “Odna zadacha ob ustoichivom otslezhivanii dvizheniya”, Tr. In-ta matem. i mekhan., 12, no. 1, UrO RAN, Ekaterinburg, 2006, 142–156