Unbiased non-simulation estimators in Monte Carlo methods and their applications in particle transport

References

• Khisamutdinov , A. I. 1970 . ‘Unit’ class of estimators for computing functionals on solution of second kind integral equation by Monte Carlo methods . Zh. Vychisl. Matem. i Matem. Fiz. , 10 ( 5 ) : 12G9 1280 (Russian); Engl. transl. in USSR Comput. Math. and Math. Phys. Vol. 10(1970)
   Google Scholar
• Khisamutdinov , A. I. 1981 . Unbiased random estimators of iterations of integral operator with exponential nonlinearity . Zh. Vychisl. Matem. i Matem. Fiz. , 21 ( 2 ) : 363 – 370 . Engl. transl. in USSR Comput. Math. and Math. Phys. Vol. 21 (1981).
   Google Scholar
• Khisamutdinov , A. I. 1986 . “ Unbiased Estimators in Monte Carlo methods for integral equations ” . 158 Novosibirsk (Russian)
   Google Scholar
• Curtiss , J. H. 1954 . Monte Carlo methods for the iteration of linear operators . J. Math. Phis. , 32 ( 4 ) : 209 – 232 .
   Web of Science ®Google Scholar
• Albert , G. E. 1956 . “ A general theory of stochastic estimates of the Neumann series for the solution of certain Fredholm integral equation and related series ” . In Symposium on Monte Carlo methods , 37 – 46 . N. Y. : Wiley .
   Google Scholar
• Berger , M. J. 1956 . “ An application of Monte Carlo method to a problem in gamma ray diffusion ” . In Symposium on Monte Carlo methods , N. Y. : Wiley .
   Google Scholar
• Spanier , J. and Gelbard , E. M. 1969 . Monte Carlo Principles and Neutron Transport Problems , Addison-Wesley Publishing Company .
   Google Scholar
• Khisamutdinov , A. I. 1967 . On effectivity of expected value method for one class problems . Zh. Vychisl. Matem. i Matem. Fiz. , 7 ( 4 ) : 946 – 953 . (Russian); Engl. transl. in USSR Comput. Math. and Math. Phys. Vol. 7 (1967)
   Google Scholar
• Khisamutdinov , A. I. 1971 . “Unit” class estimators with minimal variance. -In book Probability methods of solving mathematical physics problems 184 – 210 . Novosibirsk
   Google Scholar
• Kalos , M. H. 1963 . Monte Carlo methods for estimation of flux at a point . Nucl. Sci. and Engn. , 16 ( 1 ) : 111 – 117 .
   Web of Science ®Google Scholar
• Ermakov , S. M. and Zolotukhin , V. Gr. 1963 . Application of Monte Carlo method for shielding calculation from nuclear radiations . Problems of physics of reactor shielding, Moscow , : 171 – 182 . Russian
   Google Scholar
• Steinberg , H. A. and Kalos , M. H. 1971 . Bounded Estimators for flux at a point in Monte Carlo . Nucl. Sci. and Engn. , 44 ( 3 ) : 406 – 412 .
   Web of Science ®Google Scholar
• Khisamutdinov , A. I. and Shishmareva , S. O. Method with induced density of additional random sampling at expected value technique . Monte Carlo methods in Compt. Math. and Math. Phys. Abstacts of 7-th USSR Conference . 1985 , Novosibirsk. pp. 266 – 269 .
   Google Scholar
• Khisamutdinov , A. I. and Shishmareva , S. O. 1992 . Non-simulation estimators in Monte Carlo methods . Zh. Vychisl. Matem. i Matem. Fiz. , 32 ( 1 ) : 115 – 122 . Engl. transl. in Russia Compt. Math. and Math. Phys., Vol. 32 (1992).
   Google Scholar
• Khisamutdinov , A. I. Blankov , E. B. 1988 . “ Numerical investigation of epithermal neutron flux dependence on polymictic collector porosity in neutron-neutron log ” . In Conditionally well-posed problems of mathematical physics and analysis , 179 – 184 . Russian : Krasnojarsk, izd. of Krasnojarsk University .
   Google Scholar
• Khisamutdinov , A. I. Blankov , E. B. 1976 . An estimator with bounded variance for computing flux at a point by Monte Carlo method . Zh. Vychisl. Matem. i Matem. Fiz. , 16 ( 5 ) : 1252 – 1263 . Russian
   Google Scholar
• Khisamutdinov , A. I. and Voronin , A. F. 1985 . Monte Carlo method with additional random sampling for computation of the flux of particle at a point . Zh. Vychisl. Matem. i Matem. Fiz. , 25 ( 8 ) : 1155 – 1163 . Engl. transl. in USSR Comput. Math. and Math. Phys. Vol. 25 (1985).
   Google Scholar
• Khisamutdinov , A. I. and Ermakova , N. E. 1976 . “ On computing particle flux at a point … Preprint No. 35 ” . In Vychisl. Tsentr Sibirsk , 19 Novosibirsk : Otdel. Akad. Nauk SSSR .
   Google Scholar
• Khisamutdinov , A. I. and Gorn , N. E. “ Spatial-energy distributions of gamma-quanta of point mono-directed mono-energy source ” . In In book Shielding from ionizing radiations …. 1983 , 214 – 221 . Russian : Tbilisy .
   Google Scholar
• Khisamutdinov , A. I. and Voronin , A. F. 1990 . Spatial distribution of the epithermal neutron flux from a Cf252 source in a “borehole - formation” system . Nucl. Geophysics , 4 : 437 – 441 .
   Google Scholar