Hi, I'm trying to understand all steps did by Geman-Yor in the paper "Pricing and Hedging Double Barrier Options: A Probabilistic Approach" (attached) . I'm in trouble with some steps namely:

$\displaystyle \mathbb{E}[\int_{\sum^{(v)}_{m,M}}^\infty e^{-\theta u}(X^{(v)}_u-h)^{+}du]$
(page 6)
to the following equations (page 7 - equations 7).
She refer to Strong Markov but which properties exactly are used and where I can find it? I don't understand the steps....

Could you help me??

Stochastic Calculus - integral and expectations-paper-0-geman_yor-1996.pdf