  We analytically discuss a multiplicative noise generalization of the
Kuramoto-Sakaguchi dynamics for an assembly of globally coupled phase
oscillators. In the mean field limit, the resulting class of invariant measures
coincides with a generalized, two parameter family of angular von Mises
probability distributions which is governed by the exit law from the unit disc
of a hyperbolic drifted Brownian motion. Our dynamics offers a simple yet
analytically tractable generalization of Kuramoto-Sakaguchi dynamics with two
control parameters. We derive an exact and very compact relation between the
two control parameters at the onset of phase oscillators synchronization.
