Geodesic
Polynomial Approximations and the Monte-Carlo Method
Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 4, pp. 473-476

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A new method of computing multiple integrals is proposed, which is a generalization of the ordinary Monte-Caro method. This new method in evaluating the integral makes use of its approximate value as obtained by formulas for mechanical quadratures in accordance with a special distribution law for the integrational points. This new method in evaluating the integral makes use of its approximate value as obtained by formulas for mechanical quadratures in accordance with a special distribution law for the integrational points. It is shown that the standard deviation of the estimation may be considerably decreased, especially when the integrand possesses good differential properties. 
@article{TVP_1960_5_4_a11,
     author = {S. M. Ermakov and V. G. Zolotukhin},
     title = {Polynomial {Approximations} and the {Monte-Carlo} {Method}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {473--476},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {1960},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1960_5_4_a11/}
}
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S. M. Ermakov; V. G. Zolotukhin. Polynomial Approximations and the Monte-Carlo Method. Teoriâ veroâtnostej i ee primeneniâ, Tome 5 (1960) no. 4, pp. 473-476. http://geodesic.mathdoc.fr/item/TVP_1960_5_4_a11/