An explicit formula for the Skorokhod map on [0, a]

The Skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions. In this work, an explicit formula for the Skorokhod map Gamma(0,a) on [0,a] for any a > 0 is derived. Specifically, it is shown that on the space D[0, infinity) of right-continuous functions with left limits taking values in R, Gamma (0, a) = Lambda(a) omicron Gamma(0), where Lambda(a) : D[0, infinity) -> D [0, infinity) is defined by [Graphics] and Gamma(0): D[O, infinity) ->. D[O, infinity) is the Skorokhod map on [0, infinity), which is given explicitly by [Graphics] In addition, properties of Lambda(a) are developed and comparision properites of Gamma(0,a) are established.