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10lides with a surface. The amount of data on microscopic probabilities required for modeling heterogeneous
reactions is limited, therefore, the urgent task is to develop approaches for estimating these probabilities
based on experimental data. The work presents the results of using the DSMC method to estimate the micro-
scopic probabilities of heterogeneous reactions based on data obtained by two experimental techniques:
measurement of the gas composition at the outlet of the cylindrical channel and measurement of heat trans-
fer between a heated wire and hydrogen atmosphere.
This work was carried out under state contracts with ICMMG SB RAS (0251-2021-0002) and with IT SB RAS
(121031800218-5).
Economic and mathematical model of the dynamics of the Baikal omul population
P. G. Sorokina1,2, V. I. Zorkaltsev 1,2
1Limnological Institute SBRAS, Irkutsk
2Baikal State University, Irkutsk
Email: sorokinapg@bgu.ru
DOI 10.24412/cl-35065-2021-1-00-92
In 2017, the Russia Government imposes a restrictions on the catches of Baikal omules, which are due to a
significant reduction in its population [1]. By the way, such restrictions led to an increase in poaching and
shadow trade. Unfortunately, the assumed measures have not solved the problem of the recovery of fish
stocks. The development and study of economic measures to regulate the volume of catches of omules would
be useful. The report is devoted to an economic and mathematical model of the development of the stock of
Baikal omule, taking into account both natural fish mortality and the intensity of poaching. At the same time,
the delivery of a commercial omule on the shore of Lake Baikal from other regions and from specially estab-
lished fish-breeding plants is considered to be one of the regulators of catches, as a result of which excessive
catches of omules in oz. Baikal is no longer profitable. The report addresses methodological problems in esti-
mating individual model parameters. [2].
The research was carried out with the financial support of the RFBR project No. 19-07-00322 and within the frame-
work of the project No. state. registration ����-�19-119070190033-0, number MINOBRNAUKI 0279-2019-0003.
References
1. Anoshko P. N., Makarov M.�., V.I. Zorkaltsev, Denikina N.N., Dzyuba E.V. Limits for coregonus migratorius (Georgi,
1775) catches and likely ecological effects. South of Russia: ecology, development 2020 V. 15 no. 3, pp. 132-143.
2. Zorkaltsev V.I. Least squares method: geometric properties, alternative approaches, applications. Novosibirsk:
Nauka, 1995, 220 p.
Vector autoregressive process. Stationarity and modeling
T. M. Tovstik
Saint Petersburg State University
Email: peter.tovstik@mail.ru
DOI 10.24412/cl-35065-2021-1-00-93
The conditions for stationarity of vector processes with a discrete parameter that satisfy the autoregres-
sive equation or a mixed autoregressive and moving average model are investigated. In a mixed model, sta-
tionarity is determined by the autoregressive part of the model. Algorithms for modeling processes in the sta-
tionary case are presented.
For similar one-dimensional processes, the stationarity condition is equivalent to the fact that the charac-
teristic polynomial determined by the autoregression coefficients has roots modulo less than one.
In the vector case, Hennan [1] showed how to find the characteristic polynomial, which in the stationary
case has roots modulo less than one. In this paper, an example is given in which the roots of the characteristic
polynomial are less than one in modulus, but the process is not stationary. Additional conditions, ensuring sta-
tionarity of the process [2], are found.
References
1. Hannan E.J. Multiple time series. John Wiley and Sons. 1970, pp.575.
2. Rozanov Ju.A. Stationary random processes. M.: Nauka. 1990, 271 p.
Numerical study of randomized projective estimator and combined kernel-projective statistical estimator
N. V. Tracheva1,2, S. A. Ukhinov1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: tnv@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-94
In this talk, we discuss two particular statistical estimators. One of them is the randomized projective es-
timator which is based on the projection expansion on the orthonormal polynomial basis. Though this estima-
tor seems to be the promising one and has been applied to solve a number of problems [1, 2, 3], the conver-
sion rates vary sufficiently depending on the basis that has been chosen. Another estimation in consideration
is a combined kernel-projection statistical estimator that was suggested in work [4] for the two-dimensional
distribution density. It was constructed in the following way: for one of the variables the classical one-
dimensional kernel estimator is formed and for other � the projection estimator. The optimal parameters for
such an estimator were obtained in [5] within the assumptions made about the convergence rate of the or-
thogonal decomposition in use. The numerical study was conducted on the number of problems of atmospher-
ic optics.
This work was carried out under state contract with ICMMG SB RAS (0251-2021-0002).
References
1. Tracheva N. V., Ukhinov S. A. On the evaluation of spatial-�angular distributions of polarization characteristics of
scattered radiation // Statistical Papers. 2018. V. 59 (4), P. 1541-1557.
2. Tracheva N. V., Ukhinov S. A. A new Monte Carlo method for estimation of time asymptotic parameters of
polarized radiation // Mathematics and Computers in Simulation. 2019. V. 161, P. 84-92.
3. Rogazinsky S. V. Statistical modelling algorithm for solving the nonlinear Boltzmann equation based on the
projection method // Russian J. of Numerical Analysis and Mathematical Modelling. 2017. V. 32 (3), P. 197-202.
4. Mikhailov G. A., Tracheva N. V., Ukhinov S. A. New Statistical Kernel-Projection Estimator in the Monte Carlo
Method // DOKLADY MATHEMATICS. 2020. V. 102 (1). P. 313-317.
5. Mikhailov G. A., Tracheva N. V., Ukhinov S. A. A new kernel-projective statistical estimator in the Monte Carlo
method // Russian J. of Numerical Analysis and Mathematical Modelling. 2020. V. 35 (6), P. 341-353.
