  We formulate a phase-reduction method for a general class of noisy limit
cycle oscillators and find that the phase equation is parametrized by the ratio
between time scales of the noise correlation and amplitude relaxation of the
limit cycle. The equation naturally includes previously proposed and mutually
exclusive phase equations as special cases. The validity of the theory is
numerically confirmed. Using the method, we reveal how noise and its
correlation time affect limit cycle oscillations.
