1. LAMPERTI TRANSFORMATION: A NEW

The Lamperti transformation is a powerful tool for studying nonstationary self-similar processes via associated station-ary generators. After having discussed how the Lamperti transformation offers a new perspective on the represen-tation of nonstationary self-similar processes, we propose here to enlarge its scope in two manners. First, we show that many kinds of broken self-similarity admit Lamperti coun-terparts which are weakened forms of stationarity: a promi-nent example is that of Discrete Scale Invariance (i.e., scale invariance for some preferred scaling factors only), which is the Lamperti image of cyclostationarity. Second, we in-troduce modified versions of the original Lamperti transfor-mation in order to stationarize other forms of broken scale invariance such as local self-similarity or finite-size scale invariance based on warped dilations properties