On modeling gaussian stationary Ornstein–Uhlenbeck processes with given reliability and accuracy in Lp-spaces
DOI:
https://doi.org/10.17721/1812-5409.2024/1.9Keywords:
Modeling with given reliability and accuracy, Gaussian stationary process, Ornstein–Uhlenbeck process, spectral density of stochastic processAbstract
Even though the problem of modelling and simulation is not new it continues to be actual over time. Our computers are becoming more powerful and this allows us to use more sofisticated algorithms for more complicated problems. In this paper we constructed the model from the series decomposition of the Gaussian stationary Ornstein–Uhlenbeck process. The Ornstein-Uhlenbeck process is widely used to model reversal processes, exchange rates, asset price volatility, etc. Controlling the model’s accuracy and reliability with which it approximates the real process is important for applications. For this purpuse we have established the relation between the model’s erorr measured in the norm of Lp-space and accuracy and reliability. The classical methods and results from the general theory of stochastic processes and sub-Gaussian spaces of random variables were used in our research. Since Gaussian stochastic processes are sub-Gaussian as well, we can utilize them. For one particular case the calculations were made in order to show how our results can be used in the particular situations. The results from our paper can help to simulate and analyse the situations which the Ornstein–Uhlenbeck process fits well.
Pages of the article in the issue: 51 - 56
Language of the article: English
References
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