论文标题
在矫正中的瞬态反射布朗运动的双偏斜对称性
A dual skew symmetry for transient reflected Brownian motion in an orthant
论文作者
论文摘要
我们在多维矫正物中引入了瞬态反射的布朗运动，该运动要么在锥体的顶端吸收，要么是逃逸到无穷大的。我们解决了计算吸收概率的问题，这是过程起点的函数。我们为吸收概率提供了一种必要的条件，即接受指数产物形式，即反射矩阵的决定因素为零。我们将这种情况称为双偏斜对称性。它回忆起哈里森（Harrison）引入的著名偏斜对称性，该对称是在经常性情况下的指数固定分布的特征。双重性来自于吸收概率满足的部分微分方程对复发情况中与固定分布相关的二元方程是双重的。
We introduce a transient reflected Brownian motion in a multidimensional orthant, which is either absorbed at the apex of the cone or escapes to infinity. We address the question of computing the absorption probability, as a function of the starting point of the process. We provide a necessary and sufficient condition for the absorption probability to admit an exponential product form, namely, that the determinant of the reflection matrix is zero. We call this condition a dual skew symmetry. It recalls the famous skew symmetry introduced by Harrison, which characterizes the exponential stationary distributions in the recurrent case. The duality comes from that the partial differential equation satisfied by the absorption probability is dual to the one associated with the stationary distribution in the recurrent case.
