  We investigate theoretically the V-I characteristics and voltage noise of
superconducting tunnel junctions with small critical current via the
matrix-continued-fraction method. Special attention is paid to the large
hysteresis in the V-I characteristics and to the voltage-noise anomaly observed
in preliminary experiments. The current dependence of the voltage noise shows a
strong asymmetry between the forward and backward current ramping and a
discontinuous change of the noise close to its measured maximum occurring at
the switching current. We show that both the large hysteresis and the voltage
noise anomaly in this current-biased setup are a consequence of the influence
of junction's electromagnetic environment. Typically, the voltage-noise
dependence on the junction current parametrized by the external drive contains
a loop which is, however, not observed experimentally because of the
implementation of the junction-current ramp. Skipping a part of the loop is
responsible for the observed hysteresis as well as the noise anomaly.
