@article{TVP_2014_59_2_a2,
author = {I. A. Ibragimov and N. V. Smorodina and M. M. Faddeev},
title = {Limit theorems on convergence of expectations of functionals of sums of independent random variables to solutions},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {233--251},
year = {2014},
volume = {59},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2014_59_2_a2/}
}
TY - JOUR AU - I. A. Ibragimov AU - N. V. Smorodina AU - M. M. Faddeev TI - Limit theorems on convergence of expectations of functionals of sums of independent random variables to solutions JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2014 SP - 233 EP - 251 VL - 59 IS - 2 UR - http://geodesic.mathdoc.fr/item/TVP_2014_59_2_a2/ LA - ru ID - TVP_2014_59_2_a2 ER -
%0 Journal Article %A I. A. Ibragimov %A N. V. Smorodina %A M. M. Faddeev %T Limit theorems on convergence of expectations of functionals of sums of independent random variables to solutions %J Teoriâ veroâtnostej i ee primeneniâ %D 2014 %P 233-251 %V 59 %N 2 %U http://geodesic.mathdoc.fr/item/TVP_2014_59_2_a2/ %G ru %F TVP_2014_59_2_a2
I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. Limit theorems on convergence of expectations of functionals of sums of independent random variables to solutions. Teoriâ veroâtnostej i ee primeneniâ, Tome 59 (2014) no. 2, pp. 233-251. http://geodesic.mathdoc.fr/item/TVP_2014_59_2_a2/
[1] Chung K. L., Zhao Z., From Brownian Motion to Schrodinger's Equation, Springer-Verlag, Berlin, 1995 | MR | Zbl
[2] Freidlin M., Functional Integration and Partial Differential Equations, Princeton Univ. Press, Princeton, 1985, 545 pp. | MR | Zbl
[3] Daletskii Yu. L., Fomin S. V., Mery i differentsialnye uravneniya v funktsionalnykh prostranstvakh, Nauka, M., 1983, 383 pp.
[4] Beghin L., Orsingher E., “The distribution of the local time for “pseudoprocess” and its connection with fractional diffusion equatios”, Stochastic Process. Appl., 115:6 (2005), 1017–1040 | DOI | MR | Zbl
[5] Lachal A., “First hitting time and place for pseudo-processes driven by the equation ${\partial}/{\partial t}=\pm{\partial^N}/{\partial x^N}$ subject to a linear drift”, J. Stochastic Process. Appl., 118:1 (2008), 1–27 | DOI | MR | Zbl
[6] Glimm Dzh., Dzhaffe A., Matematicheskie metody kvantovoi fiziki. Podkhod s ispolzovaniem funktsionalnykh integralov, Mir, M., 1984, 445 pp.
[7] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, Mir, M., 1978
[8] Maslov V. P., Kompleksnye markovskie tsepi i kontinualnyi integral Feinmana, Nauka, M., 1976, 191 pp.
[9] Maslov V. P., Chebotarev A. M., “Opredelenie kontinualnogo integrala Feinmana v $p$-predstavlenii”, Dokl. AN SSSR, 229:1 (1976), 37–38 | MR | Zbl
[10] Chebotarev A. M., “O predstavlenii resheniya uravneniya Shrëdingera v vide matematicheskogo ozhidaniya funktsionalov skachkoobraznogo protsessa”, Matem. zametki, 24:5 (1978), 699–706 | MR | Zbl
[11] Ibragimov I. A., Smorodina N. V., Faddeev M. M., “Veroyatnostnyi podkhod k postroeniyu reshenii odnomernykh nachalno-kraevykh zadach”, Teoriya veroyatn. i ee primen., 58:2 (2013), 255–281 | DOI
[12] Ibragimov I. A., Smorodina N. V., Faddeev M. M., “The probabilistic approximation of the Dirichlet initial boundary value problem solution for the equation ${{\partial u}/{\partial t}= ({\sigma^2}/{2})\Delta u}$ with a complex parameter $\sigma$”, Markov Process. Related Fields (to appear)
[13] Ibragimov I. A., Smorodina N. V., Faddeev M. M., “Predelnaya teorema o skhodimosti funktsionalov ot sluchainogo bluzhdaniya k resheniyu zadachi Koshi dlya uravneniya ${\partial u}/{\partial t}=({\sigma^2}/{2})\Delta u$ s kompleksnym parametrom $\sigma$”, Zap. nauchn. sem. POMI, 420, 2013, 88–102
[14] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971, 371 pp.
[15] Titchmarsh E. Ch., Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsialnymi uravneniyami vtorogo poryadka, v. 2, IL, M., 1961, 555 pp.
[16] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973, 736 pp.
[17] Stein I. M., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973, 342 pp.
[18] Smirnov V. I., Kurs vysshei matematiki, v. 5, Nauka, M., 1959, 655 pp.
[19] 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.
[20] Agranovich M. S., Sobolevskie prostranstva, ikh obobscheniya i ellipticheskie zadachi v oblastyakh s gladkoi i lipshitsevoi granitsei, MTsNMO, M., 2013, 378 pp.