ABSTRACT

This paper is devoted to the study of a new class of non-instantaneous impulsive stochastic differential equations driven by mixed fractional Brownian motion in separable Hilbert spaces. Based on the stochastic analysis theory, analytic semigroup theory of linear operators, fractional powers of operators, and a fixed point technique, a new set of sufficient conditions are derived to ensure the existence and uniqueness of mild solutions for the proposed stochastic system. Moreover, we also investigate the asymptotic behaviour of mild solutions and controllability results for the proposed stochastic system. Finally, an example is given to demonstrate the applicability of our main results.

摘要

本文致力于研究可分离希尔伯特空间中由混合分数布朗运动驱动的一类新的非瞬时脉冲随机微分方程。基于随机分析理论、线性算子的解析半群理论、算子的分数幂和不动点技术，推导了一组新的充分条件，以保证所提出的随机系统温和解的存在性和唯一性。此外，我们还研究了所提出的随机系统的温和解的渐近行为和可控性结果。最后，给出一个例子来证明我们主要结果的适用性。