Geodesic
Vector estimators of the Monte Carlo method: dual representation and optimization
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 423-438 
G. A. Mikhailov; I. N. Medvedev. Vector estimators of the Monte Carlo method: dual representation and optimization. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 423-438. http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a5/
@article{SJVM_2010_13_4_a5,
     author = {G. A. Mikhailov and I. N. Medvedev},
     title = {Vector estimators of the {Monte} {Carlo} method: dual representation and optimization},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {423--438},
     year = {2010},
     volume = {13},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a5/}
}
TY  - JOUR
AU  - G. A. Mikhailov
AU  - I. N. Medvedev
TI  - Vector estimators of the Monte Carlo method: dual representation and optimization
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2010
SP  - 423
EP  - 438
VL  - 13
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a5/
LA  - ru
ID  - SJVM_2010_13_4_a5
ER  - 
%0 Journal Article
%A G. A. Mikhailov
%A I. N. Medvedev
%T Vector estimators of the Monte Carlo method: dual representation and optimization
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2010
%P 423-438
%V 13
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a5/
%G ru
%F SJVM_2010_13_4_a5

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

In this paper, a detailed analysis of the vector Monte-Carlo estimator theory for solving a system of integral equations is given. A dual representation for the variances of such estimators is introduced. With the dual representation we minimize the majorant mean-square error of a global solution estimator (of the histogram type). Also, for the first time we give a detailed description of the scalar Monte-Carlo algorithms for solving a system of integral equations and a comparison between the scalar and vector algorithms.

[1] Kattawar G. W., Plass G. N., “Radiation and polarization of multiple scattered light from hase and clouds”, Applied Optics, 7:8 (1968), 1519–1527 | DOI

[2] Springer-Verlag, 1980 | Zbl | Zbl

[3] Sobol I. M., “Metod Monte-Karlo dlya rascheta kritichnosti v mnogogruppovom priblizhenii”, Metod Monte-Karlo v probleme perenosa izluchenii, Atomizdat, M., 1967, 232–254 | MR

[4] Mikhailov G. A., “O sochetanii metoda konechnykh summ s metodom Monte-Karlo dlya resheniya integralnykh uravnenii 2-go roda”, Mat. zametki, 9:4 (1971), 425–434 | MR | Zbl

[5] Mikhailov G. A., Sabelfeld K. K., Chentsov N. N., “Vektorno-stokhasticheskie modeli nekotorykh zadach matematicheskoi fiziki”, Aktualnye problemy prikladnoi matematiki i matematicheskogo modelirovaniya, Nauka, Novosibirsk, 1982, 69–82 | MR

[6] Mikhailov G. A., “Vektornye metody Monte-Karlo dlya vychisleniya vozmuschenii i proizvodnykh po parametram”, ZhVMiMF, 27:9 (1987), 1311–1319 | MR

[7] Springer-Verlag, 1992 | MR

[8] Mikhailov G. A, Voitishek A. V., Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo, Izdatelskii tsentr “Akademiya”, M., 2006

[9] Mikhailov G. A., Medvedev I. N., Ispolzovanie sopryazhennykh uravnenii v metode Monte-Karlo, Izd-vo IVMiMG SO RAN, Novosibirsk, 2009

[10] Prigarin S. M., “O skhodimosti i optimizatsii funktsionalnykh otsenok metoda Monte-Karlo v prostranstvakh Soboleva”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 2:1 (1999), 57–67 | Zbl