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    Stable processes have thorns

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    Date
    2003-01
    Author
    Burdzy, Krzysztof
    Kulczycki, Tadeusz
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    Abstract
    Let X(t) be the symmetric [alpha]-stable process in R [to the power of] d, [alpha is an element of the set] (0, 2), d [is greater than or equal to] 2. For f : (0, 1) [approaching] (0,[infinity]) let D(f) be the thorn {x [is an element of the set] R [to the power of] d : x [subscript]1 [is an element of the set] (0, 1), |(x [subscript] 2, . . . , x [subscript] d)| < f(x [subscript] 1)}. 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) + [line] D(f) for all t [is an element of the set] [s, s + 1).
    URI
    http://hdl.handle.net/1773/2218
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