  This paper considers discretization of the L\'evy process appearing in the
Lamperti representation of a strictly positive self-similar Markov process.
Limit theorems for the resulting approximation are established under some
regularity assumptions on the given L\'evy process. Additionally, the scaling
limit of a positive self-similar Markov process at small times is provided.
Finally, we present an application to simulation of self-similar L\'evy
processes conditioned to stay positive.
