  For a multidimensional driftless diffusion in an unbounded, smooth,
sub-linear generalized parabolic domain, with oblique reflection from the
boundary, we give natural conditions under which either explosion occurs, if
the domain narrows sufficiently fast at infinity, or else there is
superdiffusive transience, which we quantify with a strong law of large
numbers. For example, in the case of a planar domain, explosion occurs if and
only if the area of the domain is finite. We develop and apply novel
semimartingale criteria for studying explosions and establishing strong laws,
which are of independent interest.
