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Local asymptotic self-similarity for heavy tailed harmonizable fractional Lévy motions. (English) Zbl 1478.60122

Summary: In this work we characterize the local asymptotic self-similarity of harmonizable fractional Lévy motions in the heavy tailed case. The corresponding tangent process is shown to be the harmonizable fractional stable motion. In addition, we provide sufficient conditions for existence of harmonizable fractional Lévy motions.

MSC:

60G22 Fractional processes, including fractional Brownian motion
60F05 Central limit and other weak theorems
60E07 Infinitely divisible distributions; stable distributions

Software:

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References:

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