  We introduce an invariant phase description of stochastic oscillations by
generalizing the concept of standard isophases. The average isophases are
constructed as sections in the state space, having a constant mean first return
time. The approach allows to obtain a global phase variable of noisy
oscillations, even in the cases where the phase is ill-defined in the
deterministic limit. A simple numerical method for finding the isophases is
illustrated for noise-induced switching between two coexisting limit cycles,
and for noise-induced oscillation in an excitable system. We also discuss how
to determine the isophases for experimentally observed irregular oscillations,
providing a basis for a refined phase description of observed oscillatory
dynamics.
