On the Existence of Recurrent Extensions of Self-similar Markov Processes
On the Existence of Recurrent Extensions of Self-similar Markov Processes
复制标题
论自相似马尔可夫过程的循环扩张的存在性
DOI：
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发表时间：
2006
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影响因子：
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通讯作者：
P. Fitzsimmons
中科院分区：
文献类型：
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作者：
P. Fitzsimmons
设$X=(X_T)_{tgeq0}$是一个值在非负半直线上的自相似马尔可夫过程，使得状态$0$是一个陷阱。我们给出了自相似递归扩张存在的充要条件，使得$X连续地留下$0。这一条件通过Lamperti变换用与$X$相关联的Levy过程来表示。
Let $X= (X_t) _{t geq 0}$ be a self-similar Markov process with values in the non-negative half-line, such that the state $0$ is a trap. We present a necessary and sufficient condition for the existence of a self-similar recurrent extension of $X$ that leaves $0$ continuously. This condition is expressed in terms of the Levy process associated with $X$ by the Lamperti transformation.