Geodesic
On the computation of multidimensional integrals by the Monte-Carlo method
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 738-743

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It is shown that if $W(x)$ is an arbitrary non-negative function in $R^n$ then the Markov process with the transition density $$ P(x'\to x)=\int\rho(x'\to x'')\sigma(x''\to x)\,dx'' $$ where $\rho(x'\to x)$ is an arbitraty transition density and $$ \sigma(x'\to x)=\rho(x\to x')W(x)\Big/\int\rho(x\to x')W(x)\,dx $$ has the asymptotic probability density proportional to $W(x)$. Using this fact, a method for computation of multidimensional integrals is proposed. 
@article{TVP_1971_16_4_a16,
     author = {V. F. Tur\v{c}in},
     title = {On the computation of multidimensional integrals by the {Monte-Carlo} method},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {738--743},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a16/}
}
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V. F. Turčin. On the computation of multidimensional integrals by the Monte-Carlo method. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 738-743. http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a16/