  Following an article of Dettweiler and Sabbah, this article studies the
behaviour of various Hodge invariants by middle additive convolution with a
Kummer module. The main result gives the behaviour of the nearby cycle local
Hodge numerical data at infinity. We also give expressions for Hodge numbers
and degrees of some Hodge bundles without making the hypothesis of scalar
monodromy at infinity, which generalizes the resultsof Dettweiler and Sabbah.
