多维电报方程描述的随机过程

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-03 DOI:10.1002/mma.10867

Anatoliy A. Pogorui, Ramón M. Rodríguez-Dagnino

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引用次数: 0

摘要

众所周知，许多高维电报过程的推广都是用双曲方程来描述的，其顺序取决于粒子运动可能方向的数量。然而，由Kac在他的开创性论文中首次提出的多维电报方程描述什么样的过程的问题，一直是许多学者研究的课题，迄今尚未得到完整的回答。本文利用Clifford代数的性质考虑了这类过程。

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 Processes Described by Multidimensional Telegraph Equations

It is well known that numerous generalizations of the telegraph process to higher dimensions are described by hyperbolic equations with order depending on the number of possible directions of particle's movement. However, the question of what kind of processes are described by multidimensional telegraph equations, which was first mentioned by Kac in his seminal paper, has been a topic of investigation of many scholars, and it has not been answered in a complete manner so far. In this paper, we consider such kind of processes by using properties of Clifford algebras.

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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.