Open Access
October, 1974 Transformation of Local Martingales Under a Change of Law
Jan H. Van Schuppen, Eugene Wong
Ann. Probab. 2(5): 879-888 (October, 1974). DOI: 10.1214/aop/1176996554


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.


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Jan H. Van Schuppen. Eugene Wong. "Transformation of Local Martingales Under a Change of Law." Ann. Probab. 2 (5) 879 - 888, October, 1974.


Published: October, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0321.60040
MathSciNet: MR358970
Digital Object Identifier: 10.1214/aop/1176996554

Primary: 60G45
Secondary: 60405

Keywords: Girsanov's theorem , likelihood ratio , local martingales , Martingales , Poisson process , Queueing , Wiener process

Rights: Copyright © 1974 Institute of Mathematical Statistics

Vol.2 • No. 5 • October, 1974
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