  In this paper, we establish UMD lattice-valued variational inequalities for
differential operators, ergodic averages and analytic semigroups. These results
generalize, on the one hand some scalar-valued variational inequalities in
ergodic theory, on the other hand Xu's very recent result on UMD lattice-valued
maximal inequality. As a consequence, we deduce the jump estimates and obtain
quantitative information on the rate of the pointwise convergence.
