The Annals of Probability

Radon-Nikodym Derivatives with Respect to Measures Induced by Discontinuous Independent-Increment Processes

Adrian Segall and Thomas Kailath

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Abstract

We obtain representation formulas for the Radon-Nikodym derivatives of measures absolutely continuous with respect to measures induced by processes with stationary independent increments. The proofs of these formulas, which have applications in signal detection and estimation problems, call heavily upon recent results in martingale theory, especially a general formula of Doleans-Dade for the logarithm of a strictly positive martingale in terms of a function measuring its jumps.

Article information

Source
Ann. Probab., Volume 3, Number 3 (1975), 449-464.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996352

Digital Object Identifier
doi:10.1214/aop/1176996352

Mathematical Reviews number (MathSciNet)
MR394853

Zentralblatt MATH identifier
0312.60023

JSTOR
links.jstor.org

Subjects
Primary: 60G30: Continuity and singularity of induced measures
Secondary: 60J30 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 60G45 60J75: Jump processes

Keywords
Independent increment processes Radon-Nikodym derivatives local martingales

Citation

Segall, Adrian; Kailath, Thomas. Radon-Nikodym Derivatives with Respect to Measures Induced by Discontinuous Independent-Increment Processes. Ann. Probab. 3 (1975), no. 3, 449--464. doi:10.1214/aop/1176996352. https://projecteuclid.org/euclid.aop/1176996352


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