布朗仿射逼近的矩常数
Moment Constants for Brownian Affine Approximation
中文总结 AI 辅助
本文计算布朗运动被无限制仿射函数或过原点直线均匀逼近的时间矩常数，给出前四阶矩的有理线性组合及指数积分级数，并利用时间反演联系Kingman吸收时间。
中文摘要 AI 辅助
我们评估了布朗运动被无限制仿射函数或通过原点的直线均匀逼近的时间的矩常数。前四阶矩是 $1$ 和 $\zeta(2j+1)/\pi^{2j}$（$1\le j\le4$）的有理线性组合；均值分别为 $40\zeta(3)/\pi^2-4/3$ 和 $21\zeta(3)/\pi^2$。斜率积分和共同的轮廓论证给出了无限制矩，而时间反演将锚定定律与Kingman吸收时间的倒数联系起来。对于两种模型，我们还给出了标准化绝对三阶中心矩的指数积分级数，并带有显式截断界。
英文摘要
We evaluate moment constants for the times during which Brownian motion admits uniform approximation by an unrestricted affine function or by a line through the origin. The first four moments are rational linear combinations of $1$ and $ζ(2j+1)/π^{2j}$, $1\le j\le4$; the means are $40ζ(3)/π^2-4/3$ and $21ζ(3)/π^2$, respectively. Slope integration and a common contour argument give the unrestricted moments, while time inversion relates the anchored law to the reciprocal of Kingman's absorption time. For both models we also give exponential-integral series for the standardized absolute third central moments, with explicit truncation bounds.
