英文标题：
《Representation and approximation of ambit fields in Hilbert space》
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作者：
Fred Espen Benth and Heidar Eyjolfsson
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最新提交年份：
2015
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英文摘要：
We lift ambit fields as introduced by Barndorff-Nielsen and Schmiegel to a class of Hilbert space-valued volatility modulated Volterra processes. We name this class Hambit fields, and show that they can be expressed as a countable sum of weighted real-valued volatility modulated Volterra processes. Moreover, Hambit fields can be interpreted as the boundary of the mild solution of a certain first order stochastic partial differential equation. This stochastic partial differential equation is formulated on a suitable Hilbert space of functions on the positive real line with values in the state space of the Hambit field. We provide an explicit construction of such a space. Finally, we apply this interpretation of Hambit fields to develop a finite difference scheme, for which we prove convergence under some Lipschitz conditions.
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中文摘要：
我们将Barndorff Nielsen和Schmiegel引入的范围场提升到一类Hilbert空间值波动率调制Volterra过程。我们将这类字段命名为Hambit字段，并证明它们可以表示为加权实值波动率调制Volterra过程的可数和。此外，Hambit场可以解释为一阶随机偏微分方程弱解的边界。该随机偏微分方程是在正实线上合适的希尔伯特函数空间上建立的，其值在Hambit场的状态空间中。我们提供了这样一个空间的明确构造。最后，我们应用哈姆比特场的这种解释发展了一种有限差分格式，并在一些Lipschitz条件下证明了其收敛性。
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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：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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