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The Local Structure of Random Processes
Author(s) -
Falconer Kenneth J.
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004186
Subject(s) - tangent , process (computing) , tangent vector , mathematics , limit (mathematics) , point process , tangent cone , sequence (biology) , distribution (mathematics) , point (geometry) , mathematical analysis , geometry , computer science , statistics , biology , genetics , operating system
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 Lévy processes.