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摘要翻译：
我们考虑了具有非对称跳跃分布的随机游动中破纪录事件的发生。对称随机游动中记录的统计量以前由Majumdar和Ziff分析过，并得到了很好的理解。与对称跳变分布的情况不同，在非对称跳变分布的情况下，记录的统计量取决于跳变分布的选择。我们计算记录速率$P_n(c)$，定义为第n个值大于所有以前值的概率，对于标准偏差$\sigma$被一个常数漂移$c$的高斯跳跃分布。对于小漂移，在$c/\sigma\ll n^{-1/2}$的意义上，对$P_n(c)$的校正与arctan$(\sqrt{n}）$成正比增长，并在$\frac{c}{\sqrt{2}\sigma}$的值处饱和。对于较大的$n$，记录速率接近一个常数，该常数大约由$1-(\sigma/\sqrt{2\pi}c)\textrm{exp}(-c^2/2\sigma^2)$对于$c/\sigma\gg 1$给出。这些渐近结果可推广到其他具有有限方差的连续跳跃分布。作为应用，我们将我们的分析结果与来自标准普尔500指数的366个每日股票价格的记录统计数据进行了比较。有偏随机游动在定量上解释了股票价格整体趋势导致的上部记录数量的增加，去中心化后的上部记录数量与对称随机游动有很好的一致性。然而，减损数据中较低记录的数量通过一种尚待确定的机制而显著减少。
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英文标题：
《Record statistics for biased random walks, with an application to
financial data》
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作者：
Gregor Wergen, Miro Bogner and Joachim Krug
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最新提交年份：
2011
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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英文摘要：
We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff and is well understood. Unlike the case of symmetric jump distributions, in the asymmetric case the statistics of records depends on the choice of the jump distribution. We compute the record rate $P_n(c)$, defined as the probability for the $n$th value to be larger than all previous values, for a Gaussian jump distribution with standard deviation $\sigma$ that is shifted by a constant drift $c$. For small drift, in the sense of $c/\sigma \ll n^{-1/2}$, the correction to $P_n(c)$ grows proportional to arctan$(\sqrt{n})$ and saturates at the value $\frac{c}{\sqrt{2} \sigma}$. For large $n$ the record rate approaches a constant, which is approximately given by $1-(\sigma/\sqrt{2\pi}c)\textrm{exp}(-c^2/2\sigma^2)$ for $c/\sigma \gg 1$. These asymptotic results carry over to other continuous jump distributions with finite variance. As an application, we compare our analytical results to the record statistics of 366 daily stock prices from the Standard & Poors 500 index. The biased random walk accounts quantitatively for the increase in the number of upper records due to the overall trend in the stock prices, and after detrending the number of upper records is in good agreement with the symmetric random walk. However the number of lower records in the detrended data is significantly reduced by a mechanism that remains to be identified.
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PDF链接：
https://arxiv.org/pdf/1103.0893
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