Minimax parametric optimization of numerical-statistical 'method of similar trajectories' for solution of radiation transfer theory problems

摘要

Algorithms of the 'method of similar trajectories' (MST) are implemented by a numerical-statistical simulation of the trajectories of particles, which are radiation 'quanta', according to an auxiliary radiation model and construction of weighted estimates of the functionals simultaneously for different values of 'physical' parameters. This paper is focused on the theoretical and numerical solution of the problem of choosing this auxiliary model with the aim to minimize the parametric maximum of the mean-square error of weighted estimates. We formulate new assertions concerning minimax MST algorithms and refine some previously known statements.