This article deals with the approximate controllability of semilinear retarded integrodifferential equations with non-instantaneous impulses governed by Poisson jumps in Hilbert space. The existence of a mild solution is established by using stochastic calculus and a suitable fixed point technique. The approximate controllability of the proposed non-linear stochastic differential system is obtained by employing the theory of interpolation spaces and Fredholm theory. Finally, applications to the stochastic heat equation and retarded type stochastic Benjamin–Bona–Mahony equation are provided to illustrate the developed theoretical results.

中文翻译：

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具有非瞬时脉冲的半线性延迟随机微分系统的近似可控性：Fredholm 理论方法

本文讨论了在希尔伯特空间中由泊松跳控制的具有非瞬时脉冲的半线性延迟积分微分方程的近似可控性。温和解的存在性是通过使用随机微积分和合适的不动点技术来建立的。所提出的非线性随机微分系统的近似可控性是利用插值空间理论和Fredholm理论得到的。最后，提供了对随机热方程和延迟型随机 Benjamin-Bona-Mahony 方程的应用来说明所发展的理论结果。