Weight Monte Carlo algorithms for estimation and parametric analysis of the solution to the kinetic coagulation equation
A.V. Burmistrov1, M.A. Korotchenko2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Lavrentjeva, 6, Novosibirsk, Russia, 630090
2Novosibirsk State University, Pirogova 2, Novosibirsk, Russia, 630090
Keywords: statistical modeling, evolution of many-particle system, Smoluchowski equation, value function, parametric derivative, multiplicative weight, computational cost
Abstract
The Smoluchowski equation with linear coagulation coefficients depending on two parameters is considered. We construct weight algorithms for estimating various linear functionals in an ensemble, which is governed by the equation under study. The algorithms constructed allow us to estimate the functionals for various parameters as well as parametric derivatives using the same set of trajectories. Moreover, we construct the value algorithms and analyze their efficiency for estimating the total monomer concentration as well as the total monomer and dimer concentration in the ensemble. A considerable gain in computational costs is achieved via the approximate value simulation of the time between interactions combined with the value simulation of the interacting pair number.
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