Abstract
Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic process Z whose state space in ℝ2 is given in polar coordinates by S = {(r, θ) : r ≥ 0, 0 ≤ θ ≤ ξ } for some 0 α, the strong p-variation of the sample paths of Y is finite on compact intervals, and, for 0 < p ≤ α, 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.
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More From: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
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