Girsanov showed that under an absolutely continuous change in probability measure a Wiener process is transformed into the sum of a Wiener process and a second process with sample functions which are absolutely continuous. This result has a natural generalization in the context of local martingales. This generalization is derived in this paper, and some of its ramifications are examined. As a simple application, the likelihood ratio for a single-server queueing process with very general arrival and service characteristics is derived.
Publié le : 1974-10-14
Classification:
Martingales,
local martingales,
Girsanov's theorem,
Wiener process,
Poisson process,
queueing,
likelihood ratio,
60G45,
60405
@article{1176996554,
author = {Schuppen, Jan H. Van and Wong, Eugene},
title = {Transformation of Local Martingales Under a Change of Law},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 879-888},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996554}
}
Schuppen, Jan H. Van; Wong, Eugene. Transformation of Local Martingales Under a Change of Law. Ann. Probab., Tome 2 (1974) no. 6, pp. 879-888. http://gdmltest.u-ga.fr/item/1176996554/