Components and Exit Times of Brownian Motion in Two or More p-Adic Dimensions

IF 1.2 3区 数学 Q2 MATHEMATICS, APPLIED
Rahul Rajkumar, David Weisbart
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引用次数: 2

Abstract

The fundamental solution to a pseudo-differential equation for functions defined on the d-fold product of the p-adic numbers, \(\mathbb {Q}_p\), induces an analogue of the Wiener process in \(\mathbb {Q}_p^d\). As in the real setting, the components are 1-dimensional p-adic Brownian motions with the same diffusion constant and exponent as the original process. Asymptotic analysis of the conditional probabilities shows that the vector components are dependent for all time. Exit time probabilities for the higher dimensional processes reveal a concrete effect of the component dependency.

两个或多个p进维布朗运动的分量和退出时间
对于定义在p进数的d倍积上的函数的伪微分方程的基本解\(\mathbb {Q}_p\),诱导了\(\mathbb {Q}_p^d\)中维纳过程的模拟。与实际情况一样,这些分量是一维p进布朗运动,具有与原始过程相同的扩散常数和指数。条件概率的渐近分析表明,向量分量在任何时候都是相关的。高维过程的退出时间概率揭示了组件依赖性的具体影响。
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来源期刊
CiteScore
2.10
自引率
16.70%
发文量
72
审稿时长
6-12 weeks
期刊介绍: The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics. TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers. Areas of applications include the following: antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications
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