004.94+519.218

mathematical model, information signal, conditional linear random process, characteristic function, strict sense stationary process.

The discrete-time conditional linear random process is defined, and its properties in the context of application for mathematical modelling of information signals in energy and medicine are analyzed. The relation to the continuous-time counterpart is considered on the basis of time sampling and aggregation. One-dimensional and multidimensional characteristic functions of discrete-time conditional linear random process are obtained using conditional characteristic function approach. The conditions for the investigated model to be strict sense stationary are justified.

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9. Chen P., Zhang T., Sung S. H. Strong laws for randomly weighted sums of random variables and applications in the bootstrap and random design regression. Statistica Sinica. 2019. Vol. 29. No. 4. P. 1739–1749. Doi: 10.5705/ss.202017.0106.
10. Krizmanić D. Maxima of linear processes with heavy-tailed innovations and random coefficients. Journal of Time Series Analysis. 2022. Volume 43. Issue 2. P. 238–262. Doi: https://doi.org/10.1111/jtsa.12610.
11. Demei Yuan, Lan Lei. Some results following from conditional characteristic functions. Communications in Statistics. Theory and Methods. 2013. Volume 45. Issue 12. P. 3706–3720. Doi: http://doi.org/ 10.1080/03610926.2014.906614.
12. Bulinski A. V. Conditional central limit theorem. Theory of Probability & Its Applications. 2017. Volume 6. Issue 4. P. 613–631. Doi: http://doi.org/10.1137/S0040585X97T98837X.
13. Steutel F. W. Infinitely Divisibility of Probability Distributions on the Real Line / F. W. Steutel, Klaas van Harn. Boca Raton: CRC Press, 2003. – 550 p. DOI: https://doi.org/10.1201/9780203014127
14. Gotovych V., Nazarevych O., Shcherbak L. Mathematical modeling of the regular-mode electric power supply and electric power consumption processes of the organization. Scientific Journal of TNTU. 2018. Vol. 91. No. 3. P. 134–142. Doi: https://doi.org/10.33108/visnyk_tntu2018.03.134.
15. Lytvynenko I., Lupenko S., Nazarevych O., Shymchuk H., Hotovych V. Additive mathematical model of gas consumption process. Scientific Journal of TNTU. Vol. 104. No. 4. P. 87–97.
16. Lytvynenko I. Method of the quadratic interpolation of the discrete rhythm function of the cyclical signal with a defined segment structure. Scientific Journal of TNTU. 2016. No. 4 (84). P. 131–138.

1. Babak V. P., Babak S. V., Eremenko V. S., Kuts Yu. V., Myslovych M. V., Scherbak L. M., Zaporozhets A. O. Models of Measuring Signals and Fields. Models and Measures in Measurements and Monitoring, volume 360 of Studies in Systems, Decision and Control. Springer, Cham, 2021. P. 33–59. Doi: https://doi.org/10.1007/978-3-030-70783-5_2.
2. Pierre P. A. Central Limit Theorems for Conditionally Linear Random Processes. SIAM Journal on Applied Mathematics. 1971. Vol. 20. Issue 3. P. 449–461. Doi: http://doi.org/10.1137/0120048.
3. Fryz M. Properties of conditional linear random processes and their applications in the applied problems of stochastic signal mathematical modelling. Matematychne ta kompiuterne modeliuvannia. Seriia: Tekhnichni nauky: zbirnyk naukovykh prats. 2012. Vol. 6. P. 228–238. Doi: https://doi.org/10.32626/2308-5916.2012-6.228-238. [In Ukraine].
4. Fryz M., L. Scherbak Statistical analysis of random coefficient periodic autoregression and its application for short-term electricity consumption forecasting. Tekhnichna elektrodynamika. К.: Institute of Electrodynamics National Academy of Science of Ukraine. 2019. Vol. 2. P. 38–47. Doi: https://doi.org /10.15407/techned2019.02.038. [In Ukraine].
5. Fryz M., Mlynko B. Properties of Stationarity and Cyclostationarity of Conditional Linear Random Processes. Proceedings of the 2020 IEEE 15th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET). Lviv, Slavske, Ukraine, 2020. P. 166–170. Doi: 10.1109/TCSET49122.2020.235415.
6. Iwankiewicz R. Dynamical mechanical systems under random impulses. Singapore: World Scientific Publishing Co. Pte. Ltd., 1995. 176 p. Doi: https://doi.org/10.1142/2767.
7. Barndorff-Nielsen O. E., Benth F. E., Veraart A. E. D. Ambit Stochastics. Volume 88 of Probability Theory and Stochastic Modelling. Springer Nature Switzerland AG, 2018. 402 p. Doi: https://doi.org/10.1007/978-3-319-94129-5.
8. Fryz M., Scherbak L., Karpinski M., Mlynko B. Characteristic Function of Conditional Linear Random Process. Proceedings of the 1st International Workshop on Information Technologies: Theoretical and Applied Problems. Ternopil, Ukraine, 2021. –P. 129–135. URL: https://ceur-ws.org/Vol-3039/short40.pdf.
9. Chen P., Zhang T., Sung S. H. Strong laws for randomly weighted sums of random variables and applications in the bootstrap and random design regression. Statistica Sinica. 2019. Vol. 29. No. 4. P. 1739–1749. Doi: 10.5705/ss.202017.0106.
10. Krizmanić D. Maxima of linear processes with heavy-tailed innovations and random coefficients. Journal of Time Series Analysis. 2022. Volume 43. Issue 2. P. 238–262. Doi: https://doi.org/10.1111/jtsa.12610.
11. Demei Yuan, Lan Lei. Some results following from conditional characteristic functions. Communications in Statistics. Theory and Methods. 2013. Volume 45. Issue 12. P. 3706–3720. Doi: http://doi.org/ 10.1080/03610926.2014.906614.
12. Bulinski A. V. Conditional central limit theorem. Theory of Probability & Its Applications. 2017. Volume 6. Issue 4. P. 613–631. Doi: http://doi.org/10.1137/S0040585X97T98837X.
13. Steutel F. W. Infinitely Divisibility of Probability Distributions on the Real Line / F. W. Steutel, Klaas van Harn. Boca Raton: CRC Press, 2003. – 550 p. DOI: https://doi.org/10.1201/9780203014127
14. Gotovych V., Nazarevych O., Shcherbak L. Mathematical modeling of the regular-mode electric power supply and electric power consumption processes of the organization. Scientific Journal of TNTU. 2018. Vol. 91. No. 3. P. 134–142. Doi: https://doi.org/10.33108/visnyk_tntu2018.03.134.
15. Lytvynenko I., Lupenko S., Nazarevych O., Shymchuk H., Hotovych V. Additive mathematical model of gas consumption process. Scientific Journal of TNTU. Vol. 104. No. 4. P. 87–97.
16. Lytvynenko I. Method of the quadratic interpolation of the discrete rhythm function of the cyclical signal with a defined segment structure. Scientific Journal of TNTU. 2016. No. 4 (84). P. 131–138.