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JOURNALS // Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy // Archive

Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023 Volume 10, Issue 2, Pages 187–199 (Mi vspua235)

MATHEMATICS

Stochastical computation methods and experimental designing

S. M. Ermakov, V. B. Melas

St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation

Abstract: This paper contains a brief review of the most important results obtained by the staff of the department of statistical modeling. Results include mathematical justification of computer simulation of randomness, stochastic methods of solving equations, stochastic optimization, study of stochastic stability and parallelism of Monte-Carlo algorithms. In the area of experiment planning, special attention is paid to regression experiment under nonlinear parameterization. The list of references mainly includes monographs written by members of the department. The exceptions are some articles with results not included in them.

Keywords: stochastic modeling, Monte-Carlo method, pseudorandom numbers, Markov chains, stochastic optimization, regression experiment, optimal experiment design, regression models nonlinear in parameters, functional approach, hyper exponential models, fractionally rational models, locally optimal experimental designs.

UDC: 519.6

MSC: 65C05

Received: 21.10.2022
Revised: 14.11.2022
Accepted: 17.11.2022

DOI: 10.21638/spbu01.2023.201


 English version:
Vestnik St. Petersburg University, Mathematics, 2023, 10:2, 187–199


© Steklov Math. Inst. of RAS, 2024