Mots-clés : evolution equations
@article{TVP_2016_61_4_a5,
author = {I. A. Ibragimov and N. V. Smorodina and M. M. Faddeev},
title = {Initial-boundary value problems in a~bounded domain: probabilistic representations of solutions and limit {theorems.~I}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {733--752},
year = {2016},
volume = {61},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a5/}
}
TY - JOUR AU - I. A. Ibragimov AU - N. V. Smorodina AU - M. M. Faddeev TI - Initial-boundary value problems in a bounded domain: probabilistic representations of solutions and limit theorems. I JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2016 SP - 733 EP - 752 VL - 61 IS - 4 UR - http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a5/ LA - ru ID - TVP_2016_61_4_a5 ER -
%0 Journal Article %A I. A. Ibragimov %A N. V. Smorodina %A M. M. Faddeev %T Initial-boundary value problems in a bounded domain: probabilistic representations of solutions and limit theorems. I %J Teoriâ veroâtnostej i ee primeneniâ %D 2016 %P 733-752 %V 61 %N 4 %U http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a5/ %G ru %F TVP_2016_61_4_a5
I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. Initial-boundary value problems in a bounded domain: probabilistic representations of solutions and limit theorems. I. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 733-752. http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a5/
[1] Vatanabe C., Ikeda N., Stokhasticheskie differentsialnye uravneniya i diffuzionnye protsessy, Nauka, M., 1986, 448 pp.
[2] Vatson Dzh. N., Teoriya besselevykh funktsii, Izd-vo in. lit-ry, M., 1949
[3] Gelfand I. M., Shilov G. E., Obobschennye funktsii i deistviya nad nimi, Nauka, M., 1958, 439 pp.
[4] Doob J. L., “A probabilistic approach to the heat equation”, Trans. Amer. Math. Soc., 80 (1955), 216–280 | DOI | MR | Zbl
[5] Ibragimov I. A., Smorodina N. V., Faddeev M. M., “Predelnye teoremy o skhodimosti funktsionalov ot sluchainykh bluzhdanii k resheniyu zadachi Koshi dlya uravneniya $\frac{\partial u}{ \partial t}=\frac{\sigma^2}{2}~\Delta u$ s kompleksnym parametrom $\sigma$”, Zap. nauchn. sem. POMI, 420 (2013), 88–102
[6] Ibragimov I. A., Smorodina N. V., Faddeev M. M., “Kompleksnyi analog tsentralnoi predelnoi teoremy i veroyatnostnaya approksimatsiya integrala Feinmana”, Doklady RAN, 459:3 (2014), 400–402 | DOI | Zbl
[7] Ito K., Makkin G., Diffuzionnye protsessy i ikh traektorii, Mir, M., 1968, 396 pp.
[8] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973, 736 pp.
[9] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971, 372 pp.
[10] Pilipenko A., An introduction to stochastic differential equations with reflection, Universitatsverlag, Potsdam, 2014
[11] Smirnov V. I., Kurs vysshei matematiki, chast 2, v. 3, Nauka, M., 1974, 816 pp.
[12] Skorokhod A. V., “Stokhasticheskie uravneniya dlya protsessov diffuzii s granitsami”, Teoriya veroyatn. i ee primen., 6:3 (1961), 287–298
[13] Sato K., Tanaka H., “Local times on the boundary for multi-dimensional reflecting diffusion”, Proc. Japan Acad., 38 (1961), 699–702 | DOI | MR
[14] Titchmarsh E. Ch., Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsialnymi uravneniyami vtorogo poryadka, Izd-vo in. lit-ry, M., 1961, 278 pp.
[15] Faddeev D. K., Vulikh B. Z., Uraltseva N. N. i dr., Izbrannye glavy analiza i vysshei algebry, Izd-vo Leningr. un-ta, L., 1981, 200 pp.