  Since the seminal work of Lamperti there is a lot of interest in the
understanding of the general structure of self-similar Markov processes.
Lamperti gave a representation of positive self-similar Markov processes with
initial condition strictly larger than 0 which subsequently was extended to
zero initial condition. For real self-similar Markov processes (rssMps) there
is a generalization of Lamperti's representation giving a one-to-one
correspondence between Markov additive processes and rssMps with initial
condition different from the origin. We develop fluctuation theory for Markov
additive processes and use Kuznetsov measures to construct the law of transient
real self-similar Markov processes issued from the origin. The construction
gives a pathwise representation through two-sided Markov additive processes
extending the Lamperti-Kiu representation to the origin.
