  A systematic exposition of scale functions is given for positive self-similar
Markov processes (pssMp) with one-sided jumps. The scale functions express as
convolution series of the usual scale functions associated with spectrally
one-sided L\'evy processes that underly the pssMp through the Lamperti
transform. This theory is then brought to bear on solving the spatio-temporal:
(i) two-sided exit problem; (ii) joint first passage problem upwards for the
the pssMp and its multiplicative drawdown (resp. drawup) in the spectrally
negative (resp. positive) case.

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