希尔伯特空间中分数布朗运动驱动的随机Volterra积分微分方程

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-02 DOI:10.1080/17442508.2014.924938

N. Dung

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引用次数: 17

摘要

在本文中，我们考虑了Hilbert空间中一类具有无限延迟和脉冲效应的随机Volterra积分微分方程，该方程由带有Hurst指标的分数阶布朗运动驱动。分别研究了Lipschitz脉冲和有界脉冲的情况。利用不同的不动点定理证明了温和解的存在唯一性。给出了一个例子来说明这一理论。

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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Stochastic Volterra integro-differential equations driven by fractional Brownian motion in a Hilbert space

In this article, we consider a class of stochastic Volterra integro-differential equations with infinite delay and impulsive effects, driven by fractional Brownian motion with the Hurst index in a Hilbert space. The cases of Lipschitz and bounded impulses are studied separately. The existence and uniqueness of mild solutions are proved by using different fixed-point theorems. An example is given to illustrate the theory.

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.