A. I. Khisamutdinov
On some properties of Markov processes and Monte Carlo methods for inhomogeneous Boltzmann equation
We consider Markov jump processes, Continuous Time Monte Carlo methods [A. I. Khisamutdinov, Simulation statistical modelling of the kinetic equation of rarefied gases.
Dokl. Akad. Nauk SSSR (1988) 302, 75–79 (in Russian).] based
on these processes, and the inhomogeneous smoothed Boltzmann equation. In the first place, integral
forms of a system of master equations for the processes are constructed and general properties of the
solution of the system are inspected. Secondly, we investigate unbiased simulation estimators for the
computation of linear functionals on the phase density of the average number of particles; and we
investigate the asymptotic behaviour of the variance of one of these estimators when the mean initial
number density of particles increases. Third, we touch upon the convergence of the phase density to
the solution to the Boltzmann equation. The paper considers the general case of a variable number of
particles in the system and describes an example of the application of the methods. The results have
relation to the known Direct Simulation Monte Carlo methods.
Russian Journal of Numerical Analysis and Mathematical Modelling, Walter de Gruyter
Print ISSN: 0927-6467
Volume: 20, 04/2005
Pages: 131 - 160
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