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

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.