Let T : Lp --> Lp be a positive contraction, with p strictly between 1 and
infinity. Assume that T is analytic, that is, there exists a constant K such
that \norm{T^n-T^{n-1}} < K/n for any positive integer n. Let q strictly
betweeen 2 and infinity and let v^q be the space of all complex sequences with
a finite strong q-variation. We show that for any x in Lp, the sequence
([T^n(x)](\lambda))_{n\geq 0} belongs to v^q for almost every \lambda, with an
estimate \norm{(T^n(x))_{n\geq 0}}_{Lp(v^q)}\leq C\norm{x}_p. If we remove the
analyticity assumption, we obtain a similar estimate for the ergodic averages
of T instead of the powers of T. We also obtain similar results for strongly
continuous semigroups of positive contractions on Lp-spaces
