New Monte Carlo algorithms for estimating probability moments of criticality parameters for a scattering process with multiplication in stochastic media
type: Item
instance of: scholarly article
title: New Monte Carlo algorithms for estimating probability moments of criticality parameters for a scattering process with multiplication in stochastic media
zbMATH Open document ID: 1480.65307
DOI: 10.1134/S1064562418010039
published in: Doklady Mathematics
publication date: 2018-06-20T00:00:00Z
review text: Studying Monte Carlo algorithms is very interesting due to their applications in various topics of research such as computational statistics, number theory, statistical physics, and mechanics. In this paper, the authors propose new Monte Carlo algorithms for estimating probability moments by investigating the criticality parameters for particle transport (homogeneous integrodifferential transport equation) with multiplication in a random media, particularly one-speed transport with isotropic scattering and multiplication phase function. To obtain novel results, the authors develop a randomized homogenization technique via small perturbations and diffusion approximation. The results and proofs in this work are well-organized and are written in a simple way for the readers to follow them. Two tables are provided. The first table shows the estimates of \((1-Ek)\times 10^{5}\) and \((1-Ek^{2})\times 10^{5}\) from the Monte Carlo method with their corresponding diffusion estimates. The second table shows the test estimates of the probabilities \(P(k^{n}>1)\) via the method of randomized homogenization. This paper is highly recommended for interested researchers by conducting possible related research work based on its results in the near future. Researchers can relate this interesting research topic to the topic of fractional calculus due to the importance of this topic in various modeling scenarios in physics and engineering.
Mathematics Subject Classification ID: 65M75
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35R09
zbMATH DE Number: 6892211
zbMATH Keywords: Monte Carlo
zbMATH Keywords: stochastic media
author: G. A. Mikhaĭlov
author: Galiya Z. Lotova
reviewed by: Mohammed K. A. Kaabar
MaRDI profile type: Publication
cites work: Q3242006
cites work: Q3218622
cites work: Efficient Monte Carlo algorithms for evaluating the correlation characteristics of conditional mathematical expectations
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cites work: Numerical models of mosaic homogeneous isotropic random fields and problems of radiative transfer
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full work available at URL: s1064562418010039
OpenAlex ID: W2794008589
Wikidata QID: Q130120575
description: scientific article; zbMATH DE number 6892211