罗森布拉特过程和布朗运动驱动的脉冲随机系统的近似可控性

Q3 Mathematics Ural Mathematical Journal Pub Date : 2022-12-29 DOI:10.15826/umj.2022.2.005

A. Benchaabane

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摘要

本文研究了Hilbert空间中一类由Rosenblatt过程和标准布朗运动同时驱动的脉冲随机泛函微分方程。利用Banach不动点原理证明了一个存在唯一性结果，并建立了保证温和解近似可控性的一些条件。最后给出了一个实际的例子来说明我们的结果的可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTION

In this paper we consider a class of impulsive stochastic functional differential equations driven simultaneously by a Rosenblatt process and standard Brownian motion in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the approximate controllability for the mild solution by means of the Banach fixed point principle. At the end we provide a practical example in order to illustrate the viability of our result.

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