## The Annals of Probability

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

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

Adrian Segall and Thomas Kailath

#### 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