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Local time and Tanaka formula for a multitype Dawson–Watanabe superprocess
Author(s) -
LópezMimbela José A.,
Villa Morales José
Publication year - 2006
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/mana.200310447
Subject(s) - mathematics , measure (data warehouse) , absolute continuity , local time , pure mathematics , statistics , database , computer science
In [3] Dynkin defined the local time of a continuous superprocess as a stochastic integral and gave a criterion for existence of local time. Here we prove that the conditions in Dynkin's existence criterion are satisfied by the multitype Dawson–Watanabe superprocess, and give a Tanaka formula‐like representation of the local time which is used to show that the occupation measure of the multitype superprocess is absolutely continuous with respect to an appropriate reference measure, and that the corresponding density coincides a.s. with the local time. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)