Stable Processes Have Thorns
نویسنده
چکیده
Let X(t) be the symmetric α-stable process in Rd, α ∈ (0, 2), d ≥ 2. For f : (0, 1) → (0,∞) let D(f) be the thorn {x ∈ Rd : x1 ∈ (0, 1), |(x2, . . . , xd)| < f(x1)}. We give an integral criterion in terms of f for the existence of a random time s such that X(t) remains in X(s) +D(f) for all t ∈ [s, s+ 1).
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