  Extending It\^o's formula to non-smooth functions is important both in theory
and applications. One of the fairly general extensions of the formula, known as
Meyer-It\^o, applies to one dimensional semimartingales and convex functions.
There are also satisfactory generalizations of It\^o's formula for diffusion
processes where the Meyer-It\^o assumptions are weakened even further. We study
a version of It\^o's formula for multi-dimensional finite variation L\'evy
processes assuming that the underlying function is continuous and admits weak
derivatives. We also discuss some applications of this extension, particularly
in finance.
