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SelfâIntersection Local Time for đŽâ˛(â d )âOrnsteinâUhlenbeck Processes Arising from Immigration Systems
Author(s) -
Bojdecki Tomasz,
Gorostiza Luis G.
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200205)238:1<37::aid-mana37>3.0.co;2-a
Subject(s) - ornsteinâuhlenbeck process , mathematics , intersection (aeronautics) , immigration , local time , statistical physics , stochastic process , statistics , geography , physics , cartography , archaeology
Fluctuation limits of an immigration branching particle system and an immigration branching measureâvalued process yield different types of â˛(â d )âvalued OrnsteinâUhlenbeck processes whose covariances are given in terms of an excessive measure for the underlying motion in Rd, which is taken to be a symmetric Îą âstable process. In this paper we prove existence and path continuity results for the selfâintersection local time of these OrnsteinâUhlenbeck processes. The results depend on relationships between the dimension d and the parameter Îą .