Some examples of Skorokhod embeddings obtained from the Azéma-Yor algorithm

As discussed in Madan and Yor (2002) [10], under certain conditions on a family (Hr,r>0) of Hardy-Littlewood functions, Markovian Martingales (BTHr) may be constructed. We take advantage of the explicit character of the Azéma-Yor (Skorokhod embedding) algorithm, to describe precisely some remarkable and simple examples of these Markovian Martingales.