Kasinathan, RavikumarSandrasekaran, VarshiniBaleanu, DumitruKasinathan, Ramkumar2024-05-302025-09-182024-05-302025-09-182023Kasinathan, Ramkumar...et al. "Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse", Journal of Inequalities and Applications, Vol. 2023, No. 1.1029-242Xhttps://doi.org/10.1186/s13660-023-03023-yhttps://hdl.handle.net/20.500.12416/10472The theoretical approach of random impulsive stochastic integrodifferential equations (RISIDEs) with finite delay, noncompact semigroups, and resolvent operators in Hilbert space is investigated in this article. Initially, a random impulsive stochastic integrodifferential system is proposed and the existence of a mild solution for the system is established using the Monch fixed-point theorem and contemplating Hausdorff measures of noncompactness. Then, the stability results including a continuous dependence of solutions on initial conditions, exponential stability, and Hyers-Ulam stability for the aforementioned system are investigated. Finally, an example is proposed to validate the obtained results.eninfo:eu-repo/semantics/openAccessStochastic Differential EquationsRandom ImpulseNoncompact SemigroupHyers-Ulam StabilityMean-Square Exponential StabilityArticle10.1186/s13660-023-03023-y2-s2.0-85171352141