Levy processes, which have stationary independent increments, are ideal for
modelling the various types of noise that can arise in communication channels.
If a Levy process admits exponential moments, then there exists a parametric
family of measure changes called Esscher transformations. If the parameter is
replaced with an independent random variable, the true value of which
represents a "message", then under the transformed measure the original Levy
process takes on the character of an "information process". In this paper we
develop a theory of such Levy information processes. The underlying Levy
process, which we call the fiducial process, represents the "noise type". Each
such noise type is capable of carrying a message of a certain specification. A
number of examples are worked out in detail, including information processes of
the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse
Gaussian, and normal inverse Gaussian type. Although in general there is no
additive decomposition of information into signal and noise, one is led
nevertheless for each noise type to a well-defined scheme for signal detection
and enhancement relevant to a variety of practical situations.