Geodesic
On convergence and optimization of functional Monte Carlo estimators in Sobolev spaces
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 1, pp. 57-67 
S. M. Prigarin. On convergence and optimization of functional Monte Carlo estimators in Sobolev spaces. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 1, pp. 57-67. http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a5/
@article{SJVM_1999_2_1_a5,
     author = {S. M. Prigarin},
     title = {On convergence and optimization of functional {Monte} {Carlo} estimators in {Sobolev} spaces},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {57--67},
     year = {1999},
     volume = {2},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a5/}
}
TY  - JOUR
AU  - S. M. Prigarin
TI  - On convergence and optimization of functional Monte Carlo estimators in Sobolev spaces
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 1999
SP  - 57
EP  - 67
VL  - 2
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a5/
LA  - ru
ID  - SJVM_1999_2_1_a5
ER  - 
%0 Journal Article
%A S. M. Prigarin
%T On convergence and optimization of functional Monte Carlo estimators in Sobolev spaces
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 1999
%P 57-67
%V 2
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a5/
%G ru
%F SJVM_1999_2_1_a5

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

The paper deals with the study of convergence and optimization of unbiased functional Monte Carlo estimators. We have obtained the estimators, that are optimal in Sobolev's Hilbert spaces, for calculating the integrals dependent on a parameter and for calculating the families of functionals of the solution to the integral equation of the second kind. The results have been obtained in the context of the new concept proposed by the author in order to compare the efficiency of functional estimators in Monte Carlo methods. New conditions of estimators convergence in the space of continuous functions have been proved.

[1] Frolov A. S., Chentsov N. N., “O vychislenii metodom Monte-Karlo opredelennykh integralov, zavisyaschikh ot parametra”, Zhurn. vychisl. matem. i mat. fiz., 2:4 (1962), 714–717 | MR | Zbl

[2] Prigarin S. M., “Asimptoticheskaya effektivnost otsenok v metode zavisimykh ispytanii”, Tez. dokl. VIII Vsesoyuzn. sovesch. “Metody Monte-Karlo v vychislitelnoi matematike i matematicheskoi fizike” (Novosibirsk, 1991), 94–96

[3] Ermakov S. M., Mikhailov G. A., Statisticheskoe modelirovanie, Nauka, M., 1982 | MR

[4] Paulauskas V. I., Rachkauskas A. Yu., Tochnost approksimatsii v tsentralnoi predelnoi teoreme v banakhovykh prostranstvakh, Mokslas, Vilnyus, 1987 | MR | Zbl

[5] Prigarin S. M., “Slabaya skhodimost veroyatnostnykh mer v prostranstvakh nepreryvno differentsiruemykh funktsii”, Sib. mat. zhurn., 34:1 (1993), 140–144 | MR | Zbl

[6] Prokhorov Yu. V., “Skhodimost sluchainykh protsessov i predelnye teoremy teorii veroyatnostei”, Teoriya veroyatnostei i ee primeneniya, 1:2 (1956), 178–238 | MR

[7] Billingsli P., Skhodimost veroyatnostnykh mer, Nauka, M., 1977 | MR

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

[9] Mikhailov G. A., Nazaraliev M. A., “Optimizatsiya otsenki funktsionalnykh zavisimostei metodom Monte-Karlo”, Zhurn. vychisl. matem. i mat. fiz., 10:3 (1970), 734–740

[10] Mikhailov G. A., Nekotorye voprosy teorii metodov Monte-Karlo, Nauka, Novosibirsk, 1974 | MR

[11] Ermakov S. M., Metod Monte-Karlo i smezhnye voprosy, Nauka, M., 1975 | MR | Zbl

[12] Mikhailov G. A., Minimization of computational cost of nonanalogue Monte Carlo methods, World Scientific, Singapore etc., 1991 | MR

[13] Prigarin S. M., “Convergence and optimization of functional estimates in statistical modelling in Sobolev's Hilbert spaces”, Russian J. Numer. Anal. Math. Modelling, 10:4 (1995), 325–346 | DOI | MR | Zbl

[14] Voitishek A. V., Prigarin S. M., “O funktsionalnoi skhodimosti otsenok i modelei v metode Monte-Karlo”, Zhurn. vychisl. matem. i mat. fiz., 32:10 (1992), 1641–1651 | MR