Geodesic
Variance of a standard vector Monte Carlo estimate in the theory of polarized radiative transfer
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 11, pp. 2099-2113 
G. A. Mikhailov; S. A. Uhinov; A. S. Chimaeva. Variance of a standard vector Monte Carlo estimate in the theory of polarized radiative transfer. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 11, pp. 2099-2113. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a13/
@article{ZVMMF_2006_46_11_a13,
     author = {G. A. Mikhailov and S. A. Uhinov and A. S. Chimaeva},
     title = {Variance of a~standard vector {Monte} {Carlo} estimate in the theory of polarized radiative transfer},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2099--2113},
     year = {2006},
     volume = {46},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a13/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The spectral radius $\rho$ of the matrix integral operator defining the covariance matrix of a standard vector Monte Carlo estimate in the polarized radiative transfer problem is examined. The theory of positive operators is used to analytically calculate $\rho=\rho_0$ for transfer through an infinite homogeneous medium. For a bounded medium, it is shown that $\rho$ is approximately equal to $\rho_0$ times the spectral radius of the operator corresponding to radiative transfer without polarization. This is shown numerically by estimating the iterations of the corresponding resolvent and approximately analytically by using a perturbation of a special functional.

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