arXiv subjects
Publications and source records attributed to D. G. Hobson.
In this paper we consider the Skorokhod embedding problem in Brownian motion. In particular, we give a solution based on the local time at zero of a variably skewed Brownian motion related to the underlying Brownian motion. Special cases of the construction include the Azema-Yor and Vallois embeddings. In turn, the construction has an interpretation in the Chacon-Walsh framework.
Given a Brownian motion $B_t$ and a general target law $μ$ (not necessarily centered or even integrable) we show how to construct an embedding of $μ$ in $B$. This embedding is an extension of an embedding due to Perkins, and is optimal in the sense that it simultaneously minimises the distribution of the maximum and maximises the distribution of the minimum among all embeddings of $μ$. The embedding is then applied to regular diffusions, and used to characterise the target laws for which a $H^p$-embedding may be found.