Itô's formula for finite variation Lévy processes: The case of non-smooth functions

Extending Itô'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–Itô, applies to one dimensional semimartingales and convex functions. There are also satisfactory generalizations of Itô's formula for diffusion processes where the Meyer–Itô assumptions are weakened even further. We study a version of Itô's formula for multi-dimensional finite variation Lévy processes assuming that the underlying function is continuous and admits weak derivatives. We also discuss some applications of this extension, particularly in finance.