arXiv:math/0107156v1 [math.PR] 21 Jul 2001 Sample Path Properties and Recurrence of a Stable-Like Process over an Infinite Extension of a Local Field 1 Anatoly N. Kochubei 2 Running head: “Stable-Like Process over an Infinite Extension of a Local Field” 1 This research was supported in part by CRDF Grant UM1-2090. 2 Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3, Kiev, 01601 Ukraine. E-mail: ank@ank.kiev.ua