The method of similar trajectories with branching according to parametric maximum of the auxiliary weight
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Ilia N. Medvedev
Abstract
The weighted method of similar trajectories (MST) allows one to construct estimators of functionals on a single Markov chain simultaneously for a given range of parameters of the problem. Choosing an appropriate Markov chain, we take into account additional conditions providing the finiteness of MST variance. A modification of the weighted MST with branching of chain trajectory is constructed in the paper according to the parametric maximum of the auxiliary weight. It is proved that the computational cost of this algorithm is bounded if the basis functionals are also bounded. Numerical study of the efficiency of the modified MST in comparison with analog modelling was carried out on the example of the standard problem of transfer theory on estimation of the probability of albedo and transmission of a particle.
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 5111.2014.1
Funding statement: The work was supported by the Russian Foundation for Basic Research (projects No.15–01–00894, a}, 16–01–00530, a}), the Program of Fundamental Research of the Presidium of the RAS I.33, and the Program ‘Leading scientific schools of the Russian Federation’ (project NSh–5111.2014.1)
Acknowledgements
The author is grateful to the Corr. member of the RAS G. A. Mikhailov for useful advice and remarks.
References
[1] S. M. Ermakov and G. A. Mikhailov, Statistical Modelling. Nauka, Moscow, 1982 (in Russian).Suche in Google Scholar
[2] A. S. Frolov and N. N. Chentsova, Calculation of definite integrals dependent on parameters by Monte Carlo method. Comp. Math. Math. Phys2 (1962), No. 4, 714–717.10.1016/0041-5553(63)90544-5Suche in Google Scholar
[3] G. A. Mikhailov, Optimization of Weighted Monte Carlo Methods. Springer-Verlag, Berlin–Heidelberg, 1992.10.1007/978-3-642-75981-9Suche in Google Scholar
[4] G. A. Mikhailov and I. N. Medvedev, The Use of Adjoint Equations in the Monte Carlo Method. INM&MG SB RAS, Novosibirsk, 2009 (in Russian).Suche in Google Scholar
[5] G. A. Mikhailov and S. A. Rozhenko, Parametric weighted minimax estimates in Monte Carlo methods. Comp. Math. Math. Phys53 (2013), No. 9, 1323–1335.10.1134/S0965542513090091Suche in Google Scholar
[6] I. M. Sobol’, Numerical Monte Carlo Methods. Nauka, Moscow, 1973 (in Russian).Suche in Google Scholar
© 2016 Walter de Gruyter GmbH, Berlin/Boston
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Artikel in diesem Heft
- Frontmatter
- Research Article
- Coupled atmosphere–ocean model SLAV–INMIO: implementation and first results
- Research Article
- Numerical aspects of applying the fluctuation dissipation theorem to study climate system sensitivity to external forcings
- Research Article
- On one class of high-order compact grid-characteristic schemes for linear advection
- Research Article
- Monte Carlo algorithms for calculation of diffusive characteristics of an electron avalanche in gases
- Research Article
- The method of similar trajectories with branching according to parametric maximum of the auxiliary weight
