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

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  • Shmileva, Elena

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.

Suggested Citation

  • Shmileva, Elena, 2006. "Small ball probabilities for jump Lévy processes from the Wiener domain of attraction," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1873-1881, November.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:17:p:1873-1881
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