Tempered Stable Distributions by Michael Grabchak

Author:Michael Grabchak
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.14)

Note that ν({0}) = 0 and that for α ≤ 0 we have . Note further that by (3.​14) ν is a finite measure and thus ν is a Radon measure on . We call it the extended Rosiński measure of the corresponding p-tempered α-stable distribution. From ν we get R back by

(4.15)

where is the restriction of ν to .

Remark 4.5.

Let ν be any finite Borel measure on with ν({0}) = 0. For any p > 0 and α ∈ (0, 2), ν is the extended Rosiński measure of some distribution in ETS α p . If, in addition, , then for any p > 0 and α < 2, ν is the extended Rosiński measure of some distribution in ETS α p .

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