自分解域
Selfdecomposable Fields
摘要：
本文研究了随机场的自分解性，它是直接定义的，而不是用有限维分布来定义的。在我们的分析中的主要工具是主Lévy测度和相关的Lévy-Itô表示。我们给出了类似于经典的自分解的膨胀准则。其次，我们给出了由Lévy基驱动的Volterra场是自分解的充要条件（用核函数表示）。在这方面，我们还研究了所谓的Urbanik类的随机场。我们遵循这一点的存在性和selfdecomposability的综合Volterra领域的研究。最后，我们引入了无穷可分域值Lévy过程，给出了与之相关的Lévy-Itô表示，并研究了关于这类过程的随机积分。我们提供的例子中的形式的Lévy半平稳过程的Gamma内核和Ornstein-Uhlenbeck过程。
英文摘要：
In the present paper we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master Lévy measure and the associated Lévy-Itô representation. We give the dilation criterion for selfdecomposability analogous to the classical one. Next, we give necessary and sufficient conditions (in terms of the kernel functions) for a Volterra field driven by a Lévy basis to be selfdecomposable. In this context we also study the so-called Urbanik classes of random fields. We follow this with the study of existence and selfdecomposability of integrated Volterra fields. Finally, we introduce infinitely divisible field-valued Lévy processes, give the Lévy-Itô representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of Lévy semistationary processes with a Gamma kernel and Ornstein-Uhlenbeck processes.
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