限制在曲线以下的修饰随机游动（补充材料）
Decorated Random Walk Restricted to Stay Below a Curve (Supplement Material)
摘要：
考虑一维类随机游动过程，其步长为中心高斯分布，其方差由直线上泊松过程的到达序列决定。这个过程是由独立的随机变量装饰的，这些变量在每一步都被添加，但不被累加。我们研究的概率，这样的过程，条件形成一个桥梁，停留在曲线的增长最多多项式快速远离边界，与指数小于一半。边界和渐近性。这些估计用于手稿“的结构极端水平集分支布朗运动“由同一作者，这份手稿是一个补充。
英文摘要：
We consider a one dimensional random-walk-like process, whose steps are centered Gaussians with variances which are determined according to the sequence of arrivals of a Poisson process on the line. This process is decorated by independent random variables which are added at each step, but do not get accumulated. We study the probability that such process, conditioned to form a bridge, stays below a curve which grows at most polynomially fast away from the boundaries, with exponent less than one half. Both bounds and asymptotics are derived. These estimates are used in the manuscript "the structure of extreme level sets in branching Brownian motion" by the same authors, to which this manuscript is a supplement.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
