Existence and stability results of mild solutions for random impulsive stochastic partial differential equations with noncompact semigroups

IF 1.1 2区经济学 Q3 BUSINESS, FINANCE Finance and Stochastics Pub Date : 2022-04-01 DOI:10.1080/17442508.2022.2056415

Quancheng Yang, Dan Wu, X. Shu

引用次数: 3

Abstract

In this paper, we study the existence and some stability results of mild solutions for random impulsive stochastic partial differential equations with noncompact semigroups in Hilbert spaces. Initially, we prove the existence of mild solutions by using Hausdorff measures of noncompactness and the Mönch fixed point theorem. Then, we explore the stability with continuous dependence of initial conditions, Hyers–Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, an example is given to illustrate the abstract results obtained in this paper.

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非紧半群随机脉冲随机偏微分方程温和解的存在性和稳定性结果

本文研究了Hilbert空间中具有非紧半群的随机脉冲随机偏微分方程温和解的存在性和一些稳定性结果。首先，我们利用非紧性的Hausdorff测度和Mönch不动点定理证明了温和解的存在性。然后，通过发展一些新的分析技术和建立一个改进不等式，探讨了系统具有连续依赖初始条件的稳定性、Hyers-Ulam稳定性和均方稳定性。最后，给出了一个算例来说明本文的抽象结果。

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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来源期刊

Finance and Stochastics 管理科学-数学跨学科应用

CiteScore

2.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Finance and Stochastics is to provide a high standard publication forum for research - in all areas of finance based on stochastic methods - on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance. Finance and Stochastics encompasses - but is not limited to - the following fields: - theory and analysis of financial markets - continuous time finance - derivatives research - insurance in relation to finance - portfolio selection - credit and market risks - term structure models - statistical and empirical financial studies based on advanced stochastic methods - numerical and stochastic solution techniques for problems in finance - intertemporal economics, uncertainty and information in relation to finance.

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