摘要翻译：
给出了半区间的归一化边际分布在时间趋于零时收敛于高斯极限律的条件。特别地，我们的结果适用于系数局部有界且连续的随机微分方程的解。该极限定理随后被推广到过程级的泛函中心极限定理。我们给出了这些结果在数学金融领域的两个应用：短期和短期隐含波动率偏差的到期日数字期权的定价。
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英文标题：
《Small time central limit theorems for semimartingales with applications》
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作者：
Stefan Gerhold, Max Kleinert, Piet Porkert, Mykhaylo Shkolnikov
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最新提交年份：
2012
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
  We give conditions under which the normalized marginal distribution of a semimartingale converges to a Gaussian limit law as time tends to zero. In particular, our result is applicable to solutions of stochastic differential equations with locally bounded and continuous coefficients. The limit theorems are subsequently extended to functional central limit theorems on the process level. We present two applications of the results in the field of mathematical finance: to the pricing of at-the-money digital options with short maturities and short time implied volatility skews.
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PDF链接：
https://arxiv.org/pdf/1208.4282