Infinite Divisibility for Stochastic Processes and Time Change

Ole Barndorff-Nielsen, Makoto Maejima and Ken-iti Sato ()
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Makoto Maejima: Keio University

Journal of Theoretical Probability, 2006, vol. 19, issue 2, 411-446

Abstract: 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.

Keywords: Infinite divisibility; selfdecomposability; temporal class L m property; time change; chronometer (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10959-006-0020-7

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