摘要翻译：
本文给出了Levy过程增量幂(X_{t+t_0}-X_{t_0}）n的显式混沌表示公式。Levy过程的平方可积泛函有两种不同的混沌展开形式：一种是关于补偿泊松随机测度的混沌展开形式，另一种是关于Levy过程跳跃的正交补偿幂的混沌展开形式。本文给出了(X_{t+t_0}-X_{t_0}）^n的这两种混沌展开式的显式计算公式。仿真结果验证了该表示是令人满意的。利用泰勒展开式，用(X_{t+t_0}-X_{t_0}）^n表示若干金融衍生品的CRP。
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英文标题：
《The Explicit Chaotic Representation of the powers of increments of Levy
  Processes》
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作者：
Wing Yan Yip, David Stephens, Sofia Olhede
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最新提交年份：
2007
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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：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  An explicit formula for the chaotic representation of the powers of increments, (X_{t+t_0}-X_{t_0})^n, of a Levy process is presented. There are two different chaos expansions of a square integrable functional of a Levy process: one with respect to the compensated Poisson random measure and the other with respect to the orthogonal compensated powers of the jumps of the Levy process. Computationally explicit formulae for both of these chaos expansions of (X_{t+t_0}-X_{t_0})^n are given in this paper. Simulation results verify that the representation is satisfactory. The CRP of a number of financial derivatives can be found by expressing them in terms of (X_{t+t_0}-X_{t_0})^n using Taylor's expansion.
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PDF链接：
https://arxiv.org/pdf/706.1698