olenaty

• 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), s. 14316–14333. doi: 10.1002/mma.11180. Fulltekst i vitenarkiv
• 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), s. 17–34. doi: 10.15421/142512. Fulltekst i vitenarkiv
• 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. Fulltekst i vitenarkiv Vis sammendrag

  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), s. 546–570. doi: 10.1137/23M1595308. Fulltekst i vitenarkiv Vis sammendrag

  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. s. 1–22. doi: 10.1080/17442508.2025.2541059. Fulltekst i vitenarkiv Vis sammendrag

  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. Fulltekst i vitenarkiv
• 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. Fulltekst i vitenarkiv
• 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. Fulltekst i vitenarkiv Vis sammendrag

  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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