Journal of Theoretical Probability

, Volume 19, Issue 2, pp 411–446 | Cite as

Infinite Divisibility for Stochastic Processes and Time Change

  • Ole E. Barndorff-Nielsen
  • Makoto Maejima
  • Ken-iti Sato

General results concerning infinite divisibility, selfdecomposability, and the class L m property as properties of stochastic processes are presented. A new concept called temporal selfdecomposability of stochastic processes is introduced. Lévy processes, additive processes, selfsimilar processes, and stationary processes of Ornstein–Uhlenbeck type are studied in relation to these concepts. Further, time change of stochastic processes is studied, where chronometers (stochastic processes that serve to change time) and base processes (processes to be time-changed) are independent but do not, in general, have independent increments. Conditions for inheritance of infinite divisibility and selfdecomposability under time change are given.


Infinite divisibility selfdecomposability temporal class Lm property time change chronometer 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Ole E. Barndorff-Nielsen
    • 1
  • Makoto Maejima
    • 2
  • Ken-iti Sato
    • 3
  1. 1.Department of Mathematical SciencesUniversity of Aarhus, Ny MunkegadeAarhus CDenmark
  2. 2.Department of MathematicsKeio UniversityHiyoshiJapan
  3. 3.Tenpaku-kuJapan

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