Geodesic
Vector estimators of the Monte Carlo method: dual representation and optimization
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 423-438

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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. 
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     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},
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     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a5/}
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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/