Vector estimators of the Monte Carlo method with a finite variance
-
N. Medvedev
Abstract
In this paper we study problems related to the finiteness of the variance of weighted Monte Carlo estimators for solving a system of second-kind integral equations. Modifications of the finiteness criterion for the variance of a weighted scalar estimator are based on the construction of an appropriate system of linear integral equations with ‘majorant’ kernels. A majorant criterion of the finiteness of a vector weighted estimator is given. This criterion uses a comparison of the estimator with a scalar estimator obtained by the method of randomization. It is shown that for the corresponding randomized algorithm the variance of the scalar estimator and the mean simulation time for a single trajectory are bounded if the original solution is bounded. The ability to use branching to construct a vector estimator of the solution to a system of integral equations is also studied.
© 2013 by Walter de Gruyter GmbH & Co.
Artikel in diesem Heft
- Masthead
- Mathematical problems of statistical modelling of polarized radiation transfer
- Vector estimators of the Monte Carlo method with a finite variance
- Numerical study of rainbows and glories in water-drop clouds
- Two-phase water flooding simulations on dynamic adaptive octree grids with two-point nonlinear fluxes
- A finite gradient-projective solver for a quadratic programming problem
- A model of an underground gas producer
- The Editorial Board of the Journal with deep regret is announcing the death of Academician Gurii Ivanovich MARCHUK aged 87, on March 24, 2013
Artikel in diesem Heft
- Masthead
- Mathematical problems of statistical modelling of polarized radiation transfer
- Vector estimators of the Monte Carlo method with a finite variance
- Numerical study of rainbows and glories in water-drop clouds
- Two-phase water flooding simulations on dynamic adaptive octree grids with two-point nonlinear fluxes
- A finite gradient-projective solver for a quadratic programming problem
- A model of an underground gas producer
- The Editorial Board of the Journal with deep regret is announcing the death of Academician Gurii Ivanovich MARCHUK aged 87, on March 24, 2013
