Besicovitch almost automorphic solutions in finite-dimensional distributions to stochastic semilinear differential equations driven by both Brownian and fractional Brownian motions

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Mathematical Methods in the Applied Sciences Pub Date : 2024-08-09 DOI:10.1002/mma.10403

Yongkun Li, Zhicong Bai

引用次数: 0

Abstract

In this paper, we are concerned with a stochastic semilinear differential equations driven by both Brownian motion and fractional Brownian motion. Firstly, we establish an inequality for the distance between finite-dimensional distributions of a random process at two different moments. Then, using the properties of stochastic integrals, fixed point theorems, and based on this inequality, we establish the existence and uniqueness of Besicovich almost automorphic solutions in finite-dimensional distributions for this type of semilinear equation. Finally, we provide an example to demonstrate the effectiveness of our results. Our results are new to stochastic differential equations driven by Brownian motion or stochastic differential equations driven by fractional Brownian motion.

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由布朗运动和分数布朗运动驱动的随机半线性微分方程在有限维分布中的贝西科维奇近似自形解

本文关注的是由布朗运动和分数布朗运动驱动的随机半线性微分方程。首先，我们建立了随机过程在两个不同时刻的有限维分布间距离的不等式。然后，利用随机积分的性质、定点定理，并基于这个不等式，我们建立了这类半线性方程在有限维分布中的贝西科维奇近自形解的存在性和唯一性。最后，我们举例说明了我们结果的有效性。我们的结果是布朗运动驱动的随机微分方程或分数布朗运动驱动的随机微分方程的新发现。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.

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