УДК 519.21

С.А. СЕМЕНЮК
Національний університет «Львівська політехніка», Львів, Україна,
 serhii.a.semeniuk@lpnu.ua

ЗБІЖНІСТЬ ЗА ЙМОВІРНІСТЮ ДЛЯ ЗАДАЧІ СТОХАСТИЧНОГО
ОПТИМАЛЬНОГО КЕРУВАННЯ В СХЕМІ УСЕРЕДНЕННЯ

СПИСОК ЛІТЕРАТУРИ

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2. Zhuravel I., Semenyuk S., Korobeinikova T., Romanyuk O., Reshetnik O., Maydanyuk V. Stochastic SIR model for computer worm propagation, 2025 15th International Conference on Advanced Computer Information Technologies (ACIT). Sibenik, Croatia. 2025. P. 505–508. https://doi.org/10.1109/ACIT65614.2025.11185628.
3. Samoilenko A.M., Stanzhytskyi O.M. Qualitative and asymptotic analysis of differential equations with random perturbations. Singapore, World Scientific, 2011. 324 p. https://doi.org/10.1142/8016.
4. Ankirchner S., Engelhardt S. Long term average cost control problems without ergodicity. Appl. Math. Optim. 2022. Vol. 86, N 42. https://doi.org/10.1007/s00245-022-09902-y.
5. Semenyuk S.A., Chabanyuk Y., Chypurko R.A., Lytvyn A.A. Control problem for the Markov-modulated Poisson process in the diffusion schema. Matematychni Studii. 2025. Vol. 64, N 1. P. 99–106. https://doi.org/10.30970/ms.64.1.99-106.
6. Chabanyuk Y.M., Semenyuk S.A., Khimka U.T., Chypurko R.A. Stochastic evolution under Markov-modulated Poisson perturbation in the diffusion approximation scheme. Cybern. Syst. Anal. 2025. Vol. 61, N 3. P. 443–449. https://doi.org/10.1007/s10559-025-00781-z.
7. Korolyuk V.S., Limnios N., Samoilenko I.V. Levy and Poisson approximations of switched stochastic systems by a semimartingale approach. Comptes Rendus Mathematique. 2016. Vol. 354. P. 723–728. https://doi.org/10.1016/j.crma.2016.04.008.
8. Skorokhod A.V., Hoppensteadt F.C., Salehi H. Random perturbation method with application in science and engineering. N.-Y.: Springer, 2002. 490 p. https://doi.org/10.1007/b98905.
9. Koroliouk D., Samoilenko I. Asymptotic and analytic methods in stochastic evolutionary symptoms. John Wiley & Sons. 2023. 234 p. https://doi.org/10.1002/9781394229482.
10. Chabanyuk Y., Nikitin A., Khimka U. Asymptotic analyses for complex evolutionary systems with Markov and Semi-Markov switching using approximation schemes, mathematics and statistics. John Wiley & Sons, 2020.
11. Xiaobin Sun, Longjie Xie, Yingchao Xie. Strong and weak convergence rates for slow–fast stochastic differential equations driven by α-stable process. Bernoulli, 2022. Vol. 28, N 1. P. 343–369. https://doi.org/10.3150/21-BEJ1345.
12. Shen Guangjun, Fan Jingjing, Wu Jiang-Lun, Wang Zhi. Stochastic averaging principle for neutral stochastic functional differential equations driven by G-Lvy process. Stochastics and Dynamics. 2024. Vol. 24, N 4. 2450029, https://doi.org/10.1142/S0219493724500291.
13. Yanyan Du, Yuming Chen, Qimin Zhang. Averaging principle and optimal control for a two-time-scale stochastic reaction-diffusion HIV model. Adv. Cont. Discr. Mod. 2025. Vol. 177. https://doi.org/10.1186/s13662-025-04036-1.
14. Ruomiao Huang, Danfeng Luo. Strong averaging principle for generalized Caputo fractional stochastic neutral differential equations driven by multiplicative fractional Brownian motion. Chaos. Solitons & Fractals. 2025. Vol. 201, N 1. https://doi.org/10.1016/j.chaos.2025.117179.