Voir la notice de l'article provenant de la source Math-Net.Ru
@article{TIMB_2014_22_1_a5, author = {A. D. Egorov}, title = {On composed approximate formulas for expectations of functionals of~random processes}, journal = {Trudy Instituta matematiki}, pages = {70--77}, publisher = {mathdoc}, volume = {22}, number = {1}, year = {2014}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/TIMB_2014_22_1_a5/} }
A. D. Egorov. On composed approximate formulas for expectations of functionals of~random processes. Trudy Instituta matematiki, Tome 22 (2014) no. 1, pp. 70-77. http://geodesic.mathdoc.fr/item/TIMB_2014_22_1_a5/
[1] Cameron R. H., ““Simpson's rule” for the numerical evaluation of Wiener's integrals in function space”, Duke Math. J., 18:1 (1951), 111–130 | DOI
[2] Yanovich L. A., Priblizhennoe vychislenie kontinualnykh integralov po gaussovym meram, Nauka i tekhnika, Minsk, 1976
[3] Egorov A. D., Sobolevskii P. I., Yanovich L. A., Priblizhennye metody vychisleniya kontinualnykh integralov, Nauka i tekhnika, Minsk, 1985
[4] Egorov A. D., Sobolevsky P. I., Yanovich L. A., Functional Integrals: Approximate Evaluation and Applications, Kluwer Academic Publishers, 1993
[5] Petrov V. A., “Sostavnye priblizhennye formuly dlya integralov ot funktsionalov spetsialnogo vida”, Dokl. AN BSSR, 30:2 (1986), 116–119
[6] Egorov A. D., Zhidkov E. P., Lobanov Yu. Yu., Vvedenie v teoriyu i prilozheniya funktsionalnogo integrirovaniya, Fizmatlit, M., 2006
[7] Likhoded N. A., “Utochnenie monte-karlovskoi otsenki kontinualnykh integralov”, Vestsi AN BSSR. Ser. fiz.-mat. navuk, 1990, no. 2, 8–13
[8] Egorov A. D., Zherelo A. V., “Approximations of functional integrals with respect to measure generated by solutions of stochastic differential equations”, Monte Carlo methods and applications, 10:3–4 (2004), 257–264
[9] Egorov A. D., Sabelfeld K., “Approximate formulas for expectations of functionals of solutions to stochastic differential equations”, Monte Carlo Methods and Applications, 18 (2009), 95–127
[10] Cameron R. H., Martin W. T., “The orthogonal development of non linear functionals in series of Fourier–Hermite functionals”, Ann. Math., 48 (1947), 385–392 | DOI
[11] Xiu D., Karniadakis G. E., “The Wiener–Askey polynomial chaos for stochastic differential equations”, SIAM J. Sci. Comput., 24:2 (2002), 619–644 | DOI
[12] Luo W., Wiener chaos expansion and numerical solutions of stochastic partial differential equations, Ph. D. Thesis, California Institute of Technology, 2006
[13] Lototsky S. V., Rozovskii B. L., “Wiener chaos solutions of linear stochastic equations”, Annals of Probability, 34:2 (2006), 638–662 | DOI
[14] Ma J., Protter Ph., San Martin J., “Anticipating integrals for a class of martingales”, Bernoulli, 4:1 (1998), 81–114 | DOI
[15] Kuznetsov D. F., Chislennoe integrirovanie stokhasticheskikh differentsialnykh uravnenii, SPb. gos. un-t, SPb., 2001; Физматлит, 2006