IJPAM: Volume 2, No. 2 (2002)

LIKELIHOOD RATIO DETECTION OF RANDOM
SIGNALS: THE CASE OF CAUSALLY FILTERED
AND WEIGHTED WIENER AND POISSON NOISES

A. Climescu-Haulica$^1$, A.F. Gualtierotti$^2$
$^1$Communications Research Centre
Ottawa K2H 8S2, CANADA
e-mail: adriana.climescu@crc.ca
$^2$IDHEAP, 21 Maladière, CH-1022
Chavannes-près-Renens, SWITZERLAND
e-mail: antonio.gualtierotti@idheap.unil.ch


Abstract.This paper contains first of all conditions for absolute continuity as well as a new likelihood ratio formula for detecting a random signal whose law is unknown, and which is obscured by noise that is modeled as the output of a causal filter of weighted Wiener and Poisson processes. Secondly, the derivation presented reveals, through its reproducing kernel Hilbert space framework, the reasons that make the method work, as well as its limitations. The tools used are the Cramér-Hida representation and stochastic calculus not assuming the ``usual conditions.''

Received: June 1, 2002

AMS Subject Classification: 60G35, 94A13

Key Words and Phrases: absolute continuity, likelihood ratio, detection, random signal, non-Gaussian signal and noise

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 2
Issue: 2