Positivity of Integrated Random Walks
نویسندگان
چکیده
Take a centered random walk Sn and consider the sequence of its partial sums An := ∑n i=1 Si. Suppose S1 is in the domain of normal attraction of an α-stable law with 1 < α ≤ 2. Assuming that S1 is either right-exponential (that is P(S1 > x|S1 > 0) = e−ax for some a > 0 and all x > 0) or right-continuous (skip free), we prove that P { A1 > 0, . . . , AN > 0 } ∼ CαN 1 2α− 1 2 as N → ∞, where Cα > 0 depends on the distribution of the walk. We also consider a conditional version of this problem and study positivity of integrated discrete bridges.
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