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

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• 作者：Elena Shmileva
• 关键词：Purely non-Gaussian Lé ; vy process ; Additive process ; Small deviations ; Skorokhod formula ; Density transformation of Lé ; vy processes
• 刊名：Statistics and Probability Letters
• 出版年：2006
• 期刊代码：56_01677152
• 类别：mt
• 出版时间：1 November 2006
• 卷：76
• 期：17
• 页码：1873-1881
• 文件大小：158 K

摘要

Let X_ρ be a jump Lévy process of intensity ρ which is close to the Wiener process if d2002cafd7dac5" title="Click to view the MathML source">ρ is big. We study the behavior of shifted small ball probability, namely, P{sup_t[0,1]|X_ρ(t)-λf(t)|r} under all possible relations between the parameters r→0, ρ→∞, λ→∞. The shift function 92d214f5183c" title="Click to view the MathML source">f is of bounded variation of its derivative.