Quantum tunneling and thermal activation in the parametric oscillator. P.D. Drummond, P. Kinsler Department of Physics University of Queensland Queensland 4072 Australia Phys. Rev. A 40, 4813, (1989). The mean time taken for the degenerate parametric oscillator to quantum tunnel between its two above-threshold stable states is calculated in the large photon-number limit. The result is compared to an earlier approximate result using a truncated Fokker-Planck equation in the Wigner representation. This earlier theory is equivalent to stochastic electrodynamics. Our quantum theory results indicate orders of magnitude faster tunneling far above threshold when compared to the truncated Wigner theory. Email: Dr.Paul.Kinsler@physics.org