Simulation of a strictly ?-sub-Gaussian generalized fractional Brownian motion

Vasylyk, O. I.; Lovytska, I. I.

doi:10.17721/1812-5409.2021/1.1

Simulation of a strictly ?-sub-Gaussian generalized fractional Brownian motion

Тип публікації :

Стаття

Дата випуску :

2021

Автор(и) :

Vasylyk, O. I.

Lovytska, I. I.

Мова основного тексту :

Англійська

eKNUTSHIR URL :

https://ir.library.knu.ua/handle/15071834/26054

DOI :

10.17721/1812-5409.2021/1.1

Журнал :

Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics

Випуск :

1

ISSN :

1812-5409

Початкова сторінка :

11

Кінцева сторінка :

19

Цитування :

[APA 7] Vasylyk, O. I., & Lovytska, I. I. (2021). Simulation of a strictly ?-sub-Gaussian generalized fractional Brownian motion. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 11–19. https://doi.org/10.17721/1812-5409.2021/1.1

[ДСТУ] Vasylyk O. I., Lovytska I. I. Simulation of a strictly ?-sub-Gaussian generalized fractional Brownian motion. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics. 2021. no. 1. P. 11—19. DOI: 10.17721/1812-5409.2021/1.1 (date of access: 25.07.2026).

In the paper, we consider the problem of simulation of a strictly ?-sub-Gaussian generalized fractional Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are widely used in financial and actuarial mathematics, queueing theory etc. We study some specific class of processes of generalized fractional Brownian motion and derive conditions, under which the model based on a series representation approximates a strictly ?-sub-Gaussian generalized fractional Brownian motion with given reliability and accuracy in the space C([0; 1]) in the case, when ?(x) = (|x|^p)/p, |x| ? 1, p > 1. In order to obtain these results, we use some results from the theory of ?-sub-Gaussian random processes. Necessary simulation parameters are calculated and models of sample pathes of corresponding processes are constructed for various values of the Hurst parameter H and for given reliability and accuracy using the R programming environment.
Pages of the article in the issue: 11 - 19
Language of the article: Ukrainian

Ключові слова :

φ-sub-Gaussian processes fractional Brownian motion simulation of stochastic processes accuracy and reliability of simulation φ-субгауссовi процеси дробовий броунiвський рух моделювання випадкових процесiв точнiсть i надiйнiсть моделювання

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