图enumeration中的布朗漂移区、赖特常数和其他布朗区
Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas
摘要：
本次调查汇集了不同作者对五个相关过程的面积（积分）的各种结果和公式，即\spacefactor =1000布朗运动、桥、漂移、曲折和双曲折;对于既取正值又取负值的布朗运动和桥，我们既考虑了绝对值的积分，也考虑了正（或负）部分的积分。这给了我们7个相关的正随机变量，我们研究，特别是，公式的时刻和拉普拉斯变换，我们也给（在许多情况下）系列表示和渐近的密度函数和分布函数。我们进一步研究赖特常数所产生的渐近计数的连通图，这些被称为是密切相关的时刻的布朗漂移区。主要目的是通过以平行形式陈述结果来比较这七个布朗区域的结果;从而强调相似性和差异性。一个反复出现的主题是艾里函数出现在略有不同的方式在公式中的所有七个随机变量。我们还想给出不同作者所使用的许多不同的类似符号和定义之间的明确关系。也有一些新的结果，主要是为了填补文献中留下的空白。一些简短的证明，但大多数证明被省略，而不是读者提到的原始来源。
英文摘要：
This survey is a collection of various results and formulas by different authors on the areas (integrals) of five related processes, viz.\spacefactor =1000 Brownian motion, bridge, excursion, meander and double meander; for the Brownian motion and bridge, which take both positive and negative values, we consider both the integral of the absolute value and the integral of the positive (or negative) part. This gives us seven related positive random variables, for which we study, in particular, formulas for moments and Laplace transforms; we also give (in many cases) series representations and asymptotics for density functions and distribution functions. We further study Wright's constants arising in the asymptotic enumeration of connected graphs; these are known to be closely connected to the moments of the Brownian excursion area. The main purpose is to compare the results for these seven Brownian areas by stating the results in parallel forms; thus emphasizing both the similarities and the differences. A recurring theme is the Airy function which appears in slightly different ways in formulas for all seven random variables. We further want to give explicit relations between the many different similar notations and definitions that have been used by various authors. There are also some new results, mainly to fill in gaps left in the literature. Some short proofs are given, but most proofs are omitted and the reader is instead referred to the original sources.
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