Poissonian potential measures for refracted-reflected L\'evy processes

In this paper we study the potential measures and the Laplace transforms of the occupation times of a refracted-reflected spectrally negative Lévy process when the process is observed at the arrival epochs of two independent Poisson processes.

In this case, the rates of observing the underlying process differ in time which deviates from the classical theory of Poissonian observations.

Explicit expressions for the so-called Poissonian potential measures and the Poissonian occupation times are derived in terms of (known) scale functions.

Other fluctuation identities are also derived.