  The functional Ito formula, firstly introduced by Bruno Dupire for continuous
semimartingales, might be extended in two directions: different dynamics for
the underlying process and/or weaker assumptions on the regularity of the
functional. In this paper, we pursue the former type by proving the functional
version of the Meyer-Tanaka Formula. Following the idea of the proof of the
classical time-dependent Meyer-Tanaka formula, we study the mollification of
functionals and its convergence properties. As an example, we study the running
maximum and the max-martingales of Yor and Obloj.
