Qualitative analysis of symmetric fuzzy stochastic differential equations

• Autorzy: Malinowski Marek T.

Identyfikatory

DOI

10.61822/amcs-2025-0028

• Języki publikacji: EN

Abstrakty

EN

In this paper, a special approach to stochastic differential equations is explored. Specifically, the values of the mappings involved are fuzzy sets, rather than the usual single values on the real line. Additionally, the equations under consideration are symmetric, meaning that the terms of drift and diffusion appear on both sides of the equation, which is crucial for the properties of the solutions. The primary goal of this paper is to establish certain qualitative results, such as the existence of a unique solution and stability of the solution. These results are obtained under the assumption that the coefficients of the equation satisfy a condition that is weaker than the standard Lipschitz condition. It is also noted that the results obtained can be applied to symmetric fuzzy random integral equations and deterministic symmetric fuzzy integral equations.

Słowa kluczowe

EN

fuzzy mathematics; fuzzy stochastic differential equation; fuzzy stochastic process; existence of solution; uniqueness of solution

PL

matematyka rozmyta; proces stochastyczny rozmyty; istnienie rozwiązania; niepowtarzalność rozwiązania

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2025
• Tom: Vol. 35, no. 3
• Strony: 403--416
• Opis fizyczny: Bibliogr. 40 poz.

Twórcy

autor

Malinowski Marek T.

• Department of Applied Mathematics, Tadeusz Kościuszko Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).