摘要翻译：
再次讨论了亚椭圆扩散$(x^1,...,x^d)$的密度展开式。特别是，我们对投影$(x_t^1,...,x_t^l)$的密度展开感兴趣，在$t>0$时，使用$l\leq d$。找到了取代热核渐近中已知的“不在切点内”条件的全局条件。我们的小噪声扩展允许一个“二阶”指数因子。作为应用，布朗运动的Takanobu-Watanabe展开式和Levy随机区域得到了新的启示。进一步的应用包括一些随机波动率模型中的尾部和隐含波动率渐近，在一篇论文中讨论了这一点。
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英文标题：
《Marginal density expansions for diffusions and stochastic volatility,
  part I: Theoretical Foundations》
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作者：
J. D. Deuschel, P. K. Friz, A. Jacquier, S. Violante
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最新提交年份：
2013
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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：
  Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited. In particular, we are interested in density expansions of the projection $(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions are found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptotics. Our small noise expansion allows for a "second order" exponential factor. As application, new light is shed on the Takanobu--Watanabe expansion of Brownian motion and Levy's stochastic area. Further applications include tail and implied volatility asymptotics in some stochastic volatility models, discussed in a compagnion paper.
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PDF链接：
https://arxiv.org/pdf/1111.2462