Geodesic
Modification of two-step Monte Carlo algorithms based on the symmetry of the first step
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 11, pp. 2010-2019 
G. A. Mikhailov; S. A. Rozhenko. Modification of two-step Monte Carlo algorithms based on the symmetry of the first step. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 11, pp. 2010-2019. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a8/
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     author = {G. A. Mikhailov and S. A. Rozhenko},
     title = {Modification of two-step {Monte} {Carlo} algorithms based on the symmetry of the first step},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2010--2019},
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     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Two-step Monte Carlo algorithms are modified taking into account the symmetry (i.e., invariance) of the first step about some initial vector parameter of the modeled trajectory. In the modification, the modeling of this parameter is formally transferred to the second step of the algorithm. In the “splitting method”, this means the randomization of the initial points of auxiliary trajectories. It is shown that the randomization can be improved by applying the Bellman principle.

[1] Mikhailov G. A., Voitishek A. B., Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo. Uchebnoe posobie, Izdat. tsentr “Akademiya”, M., 2006

[2] Borovkov A. A., Teoriya veroyatnostei, Nauka, M., 1986 | MR | Zbl

[3] Mikhailov G. A., “Recurrent formulae and the Bellman principle in the Monte Carlo method”, Rus. J. Numer. Analys. and Math. Modelling, 9:3 (1994), 281–300 | DOI | MR