  We consider the distribution of the duration time, the time elapsed since it
began, of a diffusion process given its present position, under the assumption
that the process began at the origin. For unbiased diffusion, the distribution
does not exist (it is identically zero) for one and two dimensional systems. We
find the explicit expression for the distribution for three and higher
dimensions and discuss the behavior of the duration time statistics: we find
that the expected duration time exists only for dimensions five and higher,
whereas the variance becomes finite for seven dimensions and above. We then
turn to the case of biased diffusion. The drift velocity introduces a new time
scale and the resulting statistics arise from the interplay of the diffusive
time scale and the drift time scale. For these systems all the moments exist
and explicit expressions are presented and discussed for the expected duration
time and its variance for all dimensions.
