  Excursion reflected Brownian motion (ERBM) is a strong Markov process defined
in a finitely connected domain $D \subset \C$ that behaves like a Brownian
motion away from the boundary of $D$ and picks a point according to harmonic
measure from infinity to reflect from every time it hits a boundary component.
We give a new construction of ERBM using its conformal invariance and discuss
the relationship between the Poisson kernel and Green's function for ERBM and
conformal maps into certain classes of finitely connected domains. One
important reason for studying ERBM is the hope that it will be a useful tool in
the study of SLE in finitely connected domains. To this end, we show how the
Poisson kernel for ERBM can be used to derive a Loewner equation for simple
curves growing in a certain class of finitely connected domains.
