The Annals of Probability

Transformation of Local Martingales Under a Change of Law

Jan H. Van Schuppen and Eugene Wong

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Abstract

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.

Article information

Source
Ann. Probab., Volume 2, Number 5 (1974), 879-888.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996554

Digital Object Identifier
doi:10.1214/aop/1176996554

Mathematical Reviews number (MathSciNet)
MR358970

Zentralblatt MATH identifier
0321.60040

JSTOR
links.jstor.org

Subjects
Primary: 60G45
Secondary: 60405

Keywords
Martingales local martingales Girsanov's theorem Wiener process Poisson process queueing likelihood ratio

Citation

Schuppen, Jan H. Van; Wong, Eugene. Transformation of Local Martingales Under a Change of Law. Ann. Probab. 2 (1974), no. 5, 879--888. doi:10.1214/aop/1176996554. https://projecteuclid.org/euclid.aop/1176996554


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