论文标题
3/4平面中的固定布朗运动：通过傅立叶变换减少到黎曼 - 希伯特问题
Stationary Brownian motion in a 3/4-plane: Reduction to a Riemann-Hilbert problem via Fourier transforms
论文作者
论文摘要
与四分之一平面模型相比，在概率文献中很少分析三分之三平面的固定反射布朗运动。在这种情况下，我们的主要结果是证明确实可以通过解决与四分之一平面中遇到的边界价值问题相同的边界值问题，直至各种二元性和对称性。主要思想是从傅立叶（而不是拉普拉斯）变换开始，从而获得两个复杂变量的单个函数的功能方程。
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.
