  Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic
process Z whose state space in R^2 is given in polar coordinates by
S={(r,theta): r >= 0, 0 <= theta <= xi} for some 0 < xi < 2 pi. Let alpha=
(theta_1+theta_2)/xi, where -pi/2 < theta_1,theta_2 < pi/2 are the directions
of reflection of Z off each of the two edges of the wedge as measured from the
corresponding inward facing normal. We prove that in the case of 1 < alpha < 2,
RBM in a wedge is a Dirichlet process. Specifically, its unique Doob-Meyer type
decomposition is given by Z=X+Y, where X is a two-dimensional Brownian motion
and Y is a continuous process of zero energy. Furthermore, we show that for p >
alpha , the strong p-variation of the sample paths of Y is finite on compact
intervals, and, for 0 < p <= alpha, the strong p-variation of Y is infinite on
[0,T] whenever Z has been started from the origin. We also show that on
excursion intervals of Z away from the origin, (Z,Y) satisfies the standard
Skorokhod problem for X. However, on the entire time horizon (Z,Y) does not
satisfy the standard Skorokhod problem for X, but nevertheless we show that it
satisfies the extended Skorkohod problem.
