Ju l 2 00 7 Hausdorff Dimension For Level Sets And k - Multiple Times By MING
نویسنده
چکیده
Let X1 t1 , X 2 t2 , · · · ,X N tN be N independent Lévy processes in IR d with their respective Lévy exponents Ψj, j = 1, 2, · · · , N . The random field Xt = X 1 t1 +X 2 t2 + · · ·+X N tN , t = (t1, t2, · · · , tN ) ∈ IR N + is called the additive Lévy process. Let λd denote Lebesgue measure in IR . Define E1 + E2 = {x+ y : x ∈ E1, y ∈ E2} for any two sets E1, E2 of IR . The following theorem has recently been proved. Theorem 1.1 Let X be any additive Lévy process in IR with Lévy exponent (Ψ1, · · · ,ΨN ). Then for any F ∈ B(IR)\{∅}, E{λd(X(IR N + ) + F )} > 0 ⇐⇒ ∫
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