关于Feller过程的几个定理：瞬时性、局部时和超压缩性
Some Theorems on Feller Processes: Transience, Local Times and Ultracontractivity
摘要：
本文给出了Feller过程的瞬时性、局部时存在性以及相应的Feller半群的超压缩性的充分条件，这些条件对于Lévy过程是尖锐的.该证明使用了局部对称化技术和Feller过程的特征函数的统一上界。作为一个副产品，我们得到稳定的过程（在R的意义下）。Bass）在具有光滑变指标$α(x)\in(0,2)$的$\R^d$上证明了一个关于指数$α(x)$的瞬变判据;如果$d=1$和$\inf_{x\in\R} α(x)\in (1,2)$，则类稳定过程有局部时.
英文摘要：
We present sufficient conditions for the transience and the existence of local times of a Feller process, and the ultracontractivity of the associated Feller semigroup; these conditions are sharp for Lévy processes. The proof uses a local symmetrization technique and a uniform upper bound for the characteristic function of a Feller process. As a byproduct, we obtain for stable-like processes (in the sense of R.\ Bass) on $\R^d$ with smooth variable index $α(x)\in(0,2)$ a transience criterion in terms of the exponent $α(x)$; if $d=1$ and $\inf_{x\in\R} α(x)\in (1,2)$, then the stable-like process has local times.
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