Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency
Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency
复制标题
范围随机学的最新进展着眼于时空随机波动性/间歇性
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Almut E. D. Veraart
中科院分区：
文献类型：
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作者：
O. Barndorff;F. Benth;Almut E. D. Veraart
境界随机学是境界场和境界过程的理论和应用的总称，是时空随机学的一个新的研究领域。本文综述了迄今为止在限界随机学方面的主要研究成果，并建立了关于限界场一般性质的新结果。此外，它发展的时空随机波动/波动范围内的字段的概念。将开发各种类型的波动率调制，从幅度的随机缩放到随机时间变化和随机措施的扩展从属关系，以及波动率/强度参数的概率和L '{e}vy混合。给出了范围字段类中具体模型规范的重要示例。
Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on general properties of ambit fields. Moreover, it develops the concept of tempo-spatial stochastic volatility/intermittency within ambit fields. Various types of volatility modulation ranging from stochastic scaling of the amplitude, to stochastic time change and extended subordination of random measures and to probability and L'{e}vy mixing of volatility/intensity parameters will be developed. Important examples for concrete model specifications within the class of ambit fields are given.