摘要翻译：
广义桥是一个随机过程的定律，它是以其路径的N个线性泛函为条件的。我们考虑这类桥的两种表示形式：正交的和规范的。正交表示是从底层过程的整个路径构造的。因此，未来的道路知识是必要的。给出了任意连续高斯过程的正交表示。在规范表示中，由桥过程和底层过程产生的过滤和线性空间是一致的。因此，不需要潜在过程的未来信息。另外，在半鞅情形下，正则桥表示与滤波和半鞅分解的扩大有关。给出了所谓的预测可逆高斯过程的正则表示。所有鞅都是微不足道的预测可逆的。一个典型的预测可逆高斯过程的非半马特例子是分数布朗运动。我们将规范的桥梁应用于内幕交易。
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英文标题：
《Generalized Gaussian Bridges》
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作者：
Tommi Sottinen and Adil Yazigi
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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：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  A generalized bridge is the law of a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations of such bridges: orthogonal and canonical.   The orthogonal representation is constructed from the entire path of the underlying process. Thus, future knowledge of the path is needed. The orthogonal representation is provided for any continuous Gaussian process.   In the canonical representation the filtrations and the linear spaces generated by the bridge process and the underlying process coincide. Thus, no future information of the underlying process is needed. Also, in the semimartingale case the canonical bridge representation is related to the enlargement of filtration and semimartingale decompositions. The canonical representation is provided for the so-called prediction-invertible Gaussian processes. All martingales are trivially prediction-invertible. A typical non-semimartingale example of a prediction-invertible Gaussian process is the fractional Brownian motion.   We apply the canonical bridges to insider trading.
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PDF链接：
https://arxiv.org/pdf/1205.3405