  Understanding and predicting the dynamical properties of systems involving
dry friction is a major concern in physics and engineering. It abounds in many
mechanical processes, from the sound produced by a violin to the screeching of
chalk on a blackboard to human infant crawling dynamics and friction-based
locomotion of a multitude of living organisms (snakes, bacteria, scallops..) to
the displacement of mechanical structures (building, bridges, nuclear plants,
massive industrial infrastructures) under earthquakes and beyond. Surprisingly,
even for low-dimensional systems, the modeling of dry friction in the presence
of random forcing has not been elucidated. In this paper, we propose a
piecewise deterministic Markov process approach modeling a system with dry
friction including different coefficients for the static and dynamic forces. In
this mathematical framework, we derive the corresponding Kolmogorov equations
and related tools to compute statistical quantities of interest related to the
distributions of the static (sticked) and dynamic phases. We show ergodicity
and provide a representation formula of the stationary measure using
independent identically distributed portions of the trajectory (excursions). We
also obtain deterministic characterizations of the Laplace transforms of the
probability density functions of the durations of the static and dynamic
phases.
