On transience of Lévy-type processes
On transience of Lévy-type processes
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论Lévy型过程的瞬态性
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发表时间：
2016
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通讯作者：
Nikola Sandrić
中科院分区：
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作者：
Nikola Sandrić
本文研究了一类与伪微分算子相关的Feller过程（即所谓的Lévy型过程）的弱瞬时性和强瞬时性.作为主要结果，我们推导出这些性质的Chung-Fuchs型条件（根据相应伪微分算子的符号），这些条件对于Lévy过程来说是尖锐的。作为结果，我们还讨论了关于状态空间维数和Pruitt指标的弱和强瞬变，从而推广了一些与椭圆扩散和稳定Lévy过程相关的著名结果.最后，在符号是径向的情况下（在协变量中），我们用Lévy测度给出了弱瞬变和强瞬变的条件。
In this paper, we study weak and strong transience of a class of Feller processes associated with pseudo-differential operators, the so-called Lévy-type processes. As a main result, we derive Chung-Fuchs type conditions (in terms of the symbol of the corresponding pseudo-differential operator) for these properties, which are sharp for Lévy processes. Also, as a consequence, we discuss the weak and strong transience with respect to the dimension of the state space and Pruitt indices, thus generalizing some well-known results related to elliptic diffusion and stable Lévy processes. Finally, in the case when the symbol is radial (in the co-variable) we provide conditions for the weak and strong transience in terms of the Lévy measures.