Probabilistic representation for a solution of initial boundary value problem for a system of parabolic equations
Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 800-809 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Probabilistic representation of the solution of an initial-boundary value problem for the system of parabolic equations is obtained. On the basis of probabilistic representation, a random process is defined and, on trajectories of the process, unbiased and $\varepsilon$-biased estimations of the solution are constructed.
Keywords: probabilities of transition; Markov chain; statistical modeling.
@article{TVP_2012_57_4_a12,
     author = {G. M. Raimova},
     title = {Probabilistic representation for a solution of initial boundary value problem for a system of parabolic equations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {800--809},
     year = {2012},
     volume = {57},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a12/}
}
TY  - JOUR
AU  - G. M. Raimova
TI  - Probabilistic representation for a solution of initial boundary value problem for a system of parabolic equations
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2012
SP  - 800
EP  - 809
VL  - 57
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a12/
LA  - ru
ID  - TVP_2012_57_4_a12
ER  - 
%0 Journal Article
%A G. M. Raimova
%T Probabilistic representation for a solution of initial boundary value problem for a system of parabolic equations
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2012
%P 800-809
%V 57
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a12/
%G ru
%F TVP_2012_57_4_a12
G. M. Raimova. Probabilistic representation for a solution of initial boundary value problem for a system of parabolic equations. Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 800-809. http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a12/

[1] Ermakov S. M., Nekrutkin V. V., Sipin A. S., Sluchainye protsessy dlya resheniya klassicheskikh uravnenii matematicheskoi fiziki, Nauka, M., 1984, 205 pp. | MR

[2] Kuptsov L. P., “Svoistva srednego i printsip maksimuma dlya parabolicheskikh uravnenii vtorogo poryadka”, Dokl. AN SSSR, 242:3 (1978), 529–532 | MR | Zbl

[3] Kurbanmuradov O., “Metody bluzhdaniya po sharoidam dlya resheniya uravneniya teploprovodnosti”, Teoriya i algoritmy statisticheskogo modelirovaniya, VTs SO AN SSSR, Novosibirsk, 1984, 67–77

[4] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp. | MR

[5] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972, 414 pp. | MR

[6] Mikhailov G. A., Optimizatsiya vesovykh metodov Monte-Karlo, Nauka, M., 1987, 239 pp. | MR

[7] Mikhailov G. A., Vesovye metody Monte-Karlo, Izd-vo SO RAN, Novosibirsk, 2000, 248 pp. | MR

[8] Meier P.-A., Veroyatnost i potentsialy, Mir, M., 1973, 324 pp.

[9] Shiryaev A. N., Veroyatnost, Nauka, M., 1989, 640 pp. | MR

[10] Rasulov A., Mascagni M., Raimova G., Monte Carlo Methods for the Solution of Linear and Nonlinear Boundary Value Problems, UWED, Tashkent, 2006, 346 pp.