Hitting probabilities of single points for processes with stationary independent increments
Hitting probabilities of single points for processes with stationary independent increments
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DOI：
10.1090/s0002-9904-1969-12245-7
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发表时间：
1969-05
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影响因子：
--
通讯作者：
H. Kesten
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文献类型：
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作者：
H. Kesten
Our purpose is to determine when h(r) is strictly positive, respectively zero. An old and obvious result is that h(r) >0 for all r if Xt is Brownian motion. Somewhat more difficult is the behavior of h(r) for symmetric stable processes of index a in dimension one. For such processes it was shown by Levy, Erdös and Kac (see [6]; also [12] for simplified proofs) that h(r) >0 for all rER il Ka^2 and h(r) =0 for all r&R if a ^ l . It will be seen that this result is typical for the general situation as well. The motivation for our study was a problem of Chung's [2], [3], which asked to solve the one-dimensional convolution equation
