  A transient stochastic process is considered strongly transient if
conditioned on returning to the starting location, the expected time it takes
to return the the starting location is finite. We characterize strong
transience for a one-dimensional random walk in a random environment. We show
that under the quenched measure transience is equivalent to strong transience,
while under the averaged measure strong transience is equivalent to
ballisticity (transience with non-zero limiting speed).
