Extremes of totally skewed stable motion

J. M. P. Albin

Statistics & Probability Letters, 1993, vol. 16, issue 3, 219-224

Abstract: Let {X(t)}t[greater-or-equal, slanted]0 be [alpha]-stable motion totally skewed to the left and with [alpha][set membership, variant][1,2). We prove that P{sup0[less-than-or-equals, slant]t[less-than-or-equals, slant]hX(t)>u}~C[alpha]P{X(h)>u} as u-->[infinity]for some constant C[alpha]. Here C[alpha]>1 for [alpha]>1 while C1=1. We also briefly study totally skewed stable Ornstein Uhlenbeck processes.

Keywords: Extrema; stable; processes; Lévy; processes (search for similar items in EconPapers)
Date: 1993
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Citations: View citations in EconPapers (6)

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