New Monte Carlo algorithms for estimating probability moments of criticality parameters for a scattering process with multiplication in stochastic media
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.
scientific article; zbMATH DE number 6892211