Small ball probabilities for jump Lévy processes from the Wiener domain of attraction

Elena Shmileva

Statistics & Probability Letters, 2006, vol. 76, issue 17, 1873-1881

Abstract: Let X[rho] be a jump Lévy process of intensity [rho] which is close to the Wiener process if [rho] is big. We study the behavior of shifted small ball probability, namely, P{supt[set membership, variant][0,1]X[rho](t)-[lambda]f(t)[less-than-or-equals, slant]r} under all possible relations between the parameters r-->0, [rho]-->[infinity], [lambda]-->[infinity]. The shift function f is of bounded variation of its derivative.

Keywords: Purely; non-Gaussian; Lévy; process; Additive; process; Small; deviations; Skorokhod; formula; Density; transformation; of; Lévy; processes (search for similar items in EconPapers)
Date: 2006
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