olenaty

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Academic Interests

Random processes, Stochastic differential equations, Asymptotic behaviour of solutions of stochastic differential equations, Applications of stochastic analysis with emphasis on mathematical finance, Limit theorems, Pseudoregularly varying functions, Information technology in teaching and knowledge control.

Teaching

STK-MAT3700 -Introduction to Mathematical Finance and Investment Theory. (Fall 2022 г.)
STK4900 - Statistical Methods and Applications (Spring 2023 г.)

Background

2019 – 2023: National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Department of Mathematical Analysis and Probability Theory (Kyiv, Ukraine). Associate Professor.

Публикации

Оn the φ− asymptotic behaviour of solutions of stochastic differential equations/ Buldygin V.V., Klesov О.I., Steinebach J.G., Тymoshenko О.А. // Theory Stoch. Process.– № 1. – P. 11–30, (2008).
On the exact order of growth of solutions of stochastic differential equations with time-dependent coefficients/ Buldygin V.V., Тymoshenko О.А. // Theory Stoch. Process. – № 2. – P. 12–22 (2010).
Unbounded solutions of stochastic differential equations with time-dependent coefficients / Кlesov О.I., Тymoshenko О.А. // Annales Univ. Sci. Budapest., Sect. Comp . – № 41. – P. 25–35, (2013).
Almost Sure Asymptotic Properties of Solutions of a Class of Non-homogeneous Stochastic Differential Equations / Кlesov О.I., Тymoshenko О.А. // In: Sadovnichiy, V., Zgurovsky, M. (eds) Modern Mathematics and Mechanics. Understanding Complex Systems. Springer, (2019).
The hybrid mathematical model for the evaluation and selection of iron ore raw materials in the context of the European Green Deal./ V Polishchuk, M Kelemen, I WŁOCH, O Tymoshenko, Y Mlavets // Acta Montanistica Slovaca 2022. – Т. 27 (2022), 1.

Tags: Stochastic analysis and finance and insurance and risk

Publications

Scientific articles and book chapters

Rahman, Ghaus ur; Tymoshenko, Olena & Nunno, Giulia Di (2025). Insights on Stochastic Dynamics for Transmission of Monkeypox: Biological and Probabilistic Behavior. Mathematical Methods in the Applied Sciences. ISSN 0170-4214. 48(15), p. 14316–14333. doi: 10.1002/mma.11180. Full text in Research Archive
Panichek, O. V. & Tymoshenko, Olena (2025). LONG-TERM DYNAMICS OF A STOCHASTIC SIRV MODEL FOR TB WITH RANDOM DISTURBANCES. Journal of Optimization, Differential Equations and their Applications. ISSN 2312-4547. 33(2), p. 17–34. doi: 10.15421/142512. Full text in Research Archive
Orlovskyi, Igor; Proske, Frank Norbert & Tymoshenko, Olena (2025). Long-time behaviors of some stochastic differential equations driven by Lévy noise. Journal of Differential Equations. ISSN 0022-0396. 442. doi: 10.1016/j.jde.2025.113561. Full text in Research Archive Show summary
Using key tools such as Itô's formula for general semi-martingales, moment estimates for Lévy-type stochastic integrals, and properties of regularly varying functions we find conditions under which solutions of a stochastic differential equation with jumps are almost surely asymptotically equivalent to a nonrandom function as .
Agram, Nacira; Øksendal, Bernt Karsten; Proske, Frank Norbert & Tymoshenko, Olena (2025). Optimal control of SPDEs driven by time-space Brownian motion. SIAM Journal of Control and Optimization. ISSN 0363-0129. 63(1), p. 546–570. doi: 10.1137/23M1595308. Full text in Research Archive Show summary
In this paper, we study the optimal control of systems where the state dynamics are governed by a stochastic partial differential equation (SPDE) driven by a two-parameter (time-space) Brownian motion, also referred to as a Brownian sheet. These equations can, for example, model the growth of an ecosystem under uncertainty. We first explore some fundamental properties of such linear SPDEs. Next, utilizing time-space white noise calculus, we derive both Pontryagin-type necessary and sufficient conditions for the optimality of the control. Finally, we illustrate our results by solving a linear-quadratic control problem and examining an optimal harvesting problem in the plane. Potential applications to machine learning and to managing random environmental influences are also discussed.
Agram, Nacira; Øksendal, Bernt Karsten; Proske, Frank Norbert & Tymoshenko, Olena (2025). A Kalman filter for linear systems driven by time-space Brownian sheet. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. p. 1–22. doi: 10.1080/17442508.2025.2541059. Full text in Research Archive Show summary
We study a linear filtering problem where the signal and observation processes are described as solutions of linear stochastic differential equations driven by time-space Brownian sheets. We derive a stochastic integral equation for the conditional value of the signal given the observation. This can be considered a time-space analogue of the classical Kalman filter. The result is illustrated with examples of the filtering problem involving noisy observations of a constant and noisy observations of the Brownian sheet.
Nunno, Giulia Di; Rahman, Ghaus ur & Tymoshenko, Olena (2024). Insights on Stochastic Dynamics for Transmission of Monkeypox: Biological and Probabilistic Behaviour. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2402.05594. Full text in Research Archive
Agram, Nacira; Øksendal, Bernt Karsten; Proske, Frank Norbert & Tymoshenko, Olena (2024). Fokker-Planck equations for conditional McKean-Vlasov systems driven by Brownian sheets. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2412.20572. Full text in Research Archive
Agram, Nacira; Øksendal, Bernt Karsten; Proske, Frank Norbert & Tymoshenko, Olena (2024). Fokker-Planck equation for McKean-Vlasov SPDEs driven by time-space Brownian sheet. arXiv.org. ISSN 2331-8422. Full text in Research Archive Show summary
In this paper, we consider a McKean-Vlasov (mean-field) stochastic partial differential equations (SPDEs) driven by a Brownian sheet. We study the propagation of chaos for a space-time Ornstein-Uhlenbeck SPDE type. Subsequently, we prove the existence and uniqueness of a nonlinear McKean-Vlasov SPDE. Finally, we establish a Fokker-Planck equation for the law of the solution of the McKean-Vlasov type SPDE driven by a time-space Brownian sheet, and we provide some examples to illustrate the results obtained.

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Published June 19, 2023 10:50 AM - Last modified Jan. 29, 2024 11:04 AM

Projects

No ongoing projects

Research groups

Risk and Stochastics