An integral representation of dilatively stable processes with independent increments

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Bhatti, T.¹  Kern, P.¹ 

[1] Heinrich Heine Univ Dusseldorf, Math Inst, Univ Str 1, D-40225 Dusseldorf, Germany

关键词: Dilative stability;    Translative stability;    Lamperti transform;    Additive process;    Random integral representation;    Wide sense Ornstein-Uhlenbeck process;    Quasi-selfsimilar process;    Time-stable process;    Infinite divisibility with respect to time;   

DOI  :  10.1016/j.spa.2016.06.006

来源: Elsevier

【 摘 要 】

Dilative stability generalizes the property of selfsimilarity for infinitely divisible stochastic processes by introducing an additional scaling in the convolution exponent. Inspired by results of Igloi (2008), we will show how dilatively stable processes with independent increments can be represented by integrals with respect to time-changed Levy processes. Via a Lamperti-type transformation these representations are shown to be closely connected to translatively stable processes of Ornstein-Uhlenbeck-type, where translative stability generalizes the notion of stationarity. The presented results complement corresponding representations for selfsimilar processes with independent increments known from the literature. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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