Unfolding the Skorohod reflection of a semimartingale
Let\(\;(U_{t})_{t\geq 0}\) be a continuous semimartingale with \(U_{0}=0,\) and \( Y_{t}=U_{t}+\sup_{s\leq t}(-U_{s}),\;t\geq 0\), the Skorohod reflection of \(U\). It is proved that on a suitable probability space there exists a continuous semimartingale \((Y_{t}^{\prime })_{t\geq 0}\;\)such\ that \(\left| Y_{t}^{\prime }\right| =Y_{t}\) and \(dY_{t}^{\prime }=\;\)sgn\( \;(Y_{t}^{\prime })dU_{t},\;t\geq 0\), This generalizes the well-known fact that the Skorohod reflection of a Wiener process is the absolute value of another Wiener process with finer filtration.
scientific article; zbMATH DE number 5522235