  A result of R. Durrett, D. Iglehart and D. Miller states that Brownian
meander is Brownian motion conditioned to stay positive for a unit of time, in
the sense that it is the weak limit, as $x$ goes to 0, of Brownian motion
started at $x>0$ and conditioned to stay positive for a unit of time. We extend
this limit theorem to the case of multidimensional Brownian motion conditioned
to stay in a smooth convex cone.
