N.Golyandina and V.Nekrutkin
Estimation errors for functionals on measure spaces
LaTeX, English (20 pp.)
65C05, Monte Carlo Methods
Abstract:
The article is devoted to investigation of bias and mean-square
deviation while estimating smooth functionals on measure spaces.
Such problems appear when one uses a Monte-Carlo procedure to solve
certain linear or nonlinear equation on measures (f.e., nonlinear
Boltzmann-like equations), and wants to estimate and diminish the part
of an error corresponding to simulation of an initial distribution.
It is shown that by means of a special variant of stratification
technique both bias and variance of this part of error
may be reduced to $o(1/n)$ instead of usual $O(n^{-1})$.
Several simple examples of stratification for linear functionals (i.e.,
integrals) are represented.
Contact E-mail address: nekr@vvn.usr.pu.ru
Also submitted to:
Stochastic simulation methods, Eds. N. Balakrishnan, S.M. Ermakov and
V.B. Melas, Birkhauser, Boston.