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Stochastic Calculus - integral and expectations

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??

Thanks!!!

Attachment 18227