3/4平面中的平稳布朗运动：通过傅立叶变换简化为Riemann-Hilbert问题

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series Pub Date : 2023-09-01 DOI:10.1016/j.indag.2022.10.008

Guy Fayolle , Sandro Franceschi , Kilian Raschel

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引用次数: 0

摘要

与四分之一平面模拟模型相比，概率文献中很少分析四分之三平面中的平稳反射布朗运动。在这种情况下，我们的主要结果是证明，平稳分布确实可以通过求解与四分之一平面中遇到的边值问题相同的边值，直到各种对偶和对称性来找到。其主要思想是从傅立叶（而不是拉普拉斯）变换开始，从而获得两个复变量的单个函数的函数方程。

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Stationary Brownian motion in a 3/4-plane: Reduction to a Riemann–Hilbert problem via Fourier transforms

The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In this context, our main result is to prove that the stationary distribution can indeed be found by solving a boundary value problem of the same kind as the one encountered in the quarter plane, up to various dualities and symmetries. The main idea is to start from Fourier (and not Laplace) transforms, allowing to get a functional equation for a single function of two complex variables.

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来源期刊

Indagationes Mathematicae-New Series 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

79 days

期刊介绍： Indagationes Mathematicae is a peer-reviewed international journal for the Mathematical Sciences of the Royal Dutch Mathematical Society. The journal aims at the publication of original mathematical research papers of high quality and of interest to a large segment of the mathematics community. The journal also welcomes the submission of review papers of high quality.