Stochastics ( IF 0.8 ) Pub Date : 2019-11-29 , DOI: 10.1080/17442508.2019.1697270 Zhi Li 1 , Liping Xu 1 , Litan Yan 2
In this paper, we are concerned with a class of coupled neutral stochastic partial differential equations driven by fractional Brownian motion with Hurst parameter . On account of the Perov's fixed point theorem and semigroup theory, we prove the existence and uniqueness of mild solution. Subsequently, by using delay integral inequalities, we identify the global attracting sets of the equations under investigation. Furthermore, we obtain some sufficient conditions that ensure the exponential decay of mild solutions in the pth moment. Lastly, we present an example to illustrate our theory in this work.
中文翻译:
由分数布朗运动驱动的耦合中性SPDE的整体吸引集和指数衰减
在本文中,我们关注一类由带有Hurst参数的分数布朗运动驱动的耦合中立随机偏微分方程。 。基于佩罗夫不动点定理和半群理论,我们证明了温和解的存在性和唯一性。随后,通过使用延迟积分不等式,我们确定了所研究方程的全局吸引集。此外,我们获得了一些足够的条件,可确保在p时刻温和溶液的指数衰减。最后,我们给出一个例子来说明我们在这项工作中的理论。