  Non-equilibrium stationary fluctuations may exhibit a special symmetry called
fluctuation relations (FR). Here, we show that this property is always
satisfied by the subtraction of two random and independent variables related by
a thermodynamic-like change of measure. Taking one of them as a modulated
Poisson process, it is demonstrated that intermittence and FR are compatibles
properties that may coexist naturally. Strong non-Gaussian features
characterize the probability distribution and its generating function. Their
associated large deviation functions (LDF) develop a kink at the origin and a
plateau regime respectively. Application of this model in different stationary
nonequilibrium situations is discussed.
