  We study the stochastic motion of active particles that undergo spontaneous
transitions between two distinct modes of motion. Each mode is characterized by
a velocity distribution and an arbitrary (anti-)persistence. We present an
analytical formalism to provide a quantitative link between these two
microscopic statistical properties of the trajectory and macroscopically
observable transport quantities of interest. For exponentially distributed
residence times in each state, we derive analytical expressions for the initial
anomalous exponent, the characteristic crossover time to the asymptotic
diffusive dynamics, and the long-term diffusion constant. We also obtain an
exact expression for the time evolution of the mean square displacement over
all time scales and provide a recipe to obtain higher displacement moments. Our
approach enables us to disentangle the combined effects of velocity,
persistence, and switching probabilities between the two states on the
kinematics of particles in a wide range of stochastic active/passive processes
and to optimize the transport quantities of interest with respect to any of the
particle dynamics properties.
