  Motivated by various recent experimental findings, we propose a dynamical
model of intermittently self-propelled particles: active particles that
recurrently switch between two modes of motion, namely an active run-state and
a turn state, in which self-propulsion is absent. The durations of these
motility modes are derived from arbitrary waiting-time distributions. We derive
the expressions for exact forms of transport characteristics like mean-square
displacements and diffusion coefficients to describe such processes.
Furthermore, the conditions for the emergence of sub- and superdiffusion in the
long-time limit are presented. We give examples of some important processes
that occur as limiting cases of our system, including run-and-tumble motion of
bacteria, L\'evy walks, hop-and-trap dynamics, intermittent diffusion and
continuous time random walks.
