The local structure of random processes

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62 Citations (Scopus)

Abstract

A tangent process of a random process X at a point z is defined to be the limit in distribution of some sequence of scaled enlargements of X about z. The main result of the paper is that a tangent process must be self-similar with stationary increments, at almost all points z where the tangent process is essentially unique. The consequences for tangent processes of certain classes of process are examined, including stable processes and processes with independent increments where unique tangent processes are Levy processes.

Original languageEnglish
Pages (from-to)657-672
Number of pages16
JournalJournal of the London Mathematical Society
Volume67
Issue number3
DOIs
Publication statusPublished - Jun 2003

Keywords

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