This article concerns a class of Ornstein-Uhlenbeck type Markov processes and for which the level sets will be approached. By constructing a new class f processes,we shall obtain an inequality on the Hausdorff dimensions of the level sets for the Ornstein-Uhlenbeck type Markov processes. Based on this result, we finally verify that any two independent O-U.M.P with α-stable processes could collide with probability one.
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