  A nondissipative supercurrent state of a Josephson junction is metastable
with respect to the formation of a finite-resistance state. This transition is
driven by fluctuations, thermal at high temperatures and quantum at low
temperatures. We evaluate the life time of such a state due to quantum
fluctuations in the limit when the supercurrent is approaching the critical
current. The decay probability is determined by the instanton action for the
superconducting phase difference across the junction. At low temperatures,
dynamics of the phase is massive and is determined by the effective
capacitance, which is a sum of the geometric and intrinsic capacitance of the
junction. We model the central part of the Josephson junction either by an
arbitrary short mesoscopic conductor described by the set of its transmission
coefficients, or by a diffusive wire of an arbitrary length. The intrinsic
capacitance can generally be estimated as $C_* \sim G/E_g$, where $G$ is the
normal-state conductance of the junction and $E_g$ is the proximity minigap in
its normal part. The obtained capacitance is sufficiently large to
qualitatively explain hysteretic behavior of the current-voltage characteristic
even in the absence of overheating.
