# The development of software for simulation of random processes with a given accuracy and reliability

### Abstract

Today, the theory of random processes and time series prediction is widely used in various fields of science, not only in natural fields. That is why one of the urgent problems is to build a mathematical model of a random process and study its properties. Numerical modeling tasks become especially important due to the powerful capabilities of computer technology, which allows you to create software modeling tools and predict the behavior of a random process. There are different methods of modeling random processes and fields. In some works related to the modeling of random processes, the issues of accuracy and reliability have not been studied. In [1, 2, 3] for various stochastic processes and fields this problem was investigated. In this paper the question of accuracy and reliability of the constructed model is considered. This means that we first build the model and then test it using some adequacy tests with known accuracy and reliability. We also find the estimators of the model parameters using methods of moments. All theoretical results are applied to develop software for model construction of stochastic processes.

* Key words*: simulation, accuracy, reliability, estimation.

* Pages of the article in the issue*: 83 - 87

** Language of the article**: Ukrainian

### References

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KOZACHENKO Yu., POGORILYAK O., ROZORA I. AND TEGZA A. (2016) Simulation of Stochastic Processes with Given Accuracy and Reliability, ISTE Press - Elsevier.

KOZACHENKO, YU., ROZORA, I. (2003) Simulation of Gaussian stochastic processes, Random Oper. and Stochastic Equ., 11, №.3, 275–296.

KOZACHENKO YU., ROZORA I. (2015) On cross-correlogram estimators of impulse response functions Theor. Probability and Math. Statist., 93, 75-86.

ROZORA I., LYZHECHKO M. (2018) On the modeling of linear system input stochastic processes with given accuracy and reliability, Monte Carlo Methods Appl., 24, №. 2, 129–137.

ROZORA I. (2018) On simulation accuracy and reliability in the space L1,([0, T]) for the input Gaussian process served by the linear system taking into account the output, Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics, №. 2, 75–80.

*Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics*, (1-2), 83-87. https://doi.org/10.17721/1812-5409.2020/1-2.14

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