From Tanaka's formula to Itô's formula: The fundamental theorem of stochastic calculus (Q1386780)

The question is stated and solved: Can one deduce the (multidimensional) Itô formula from properties of local times? The answer is ``yes''. The proof uses Fubini's theorem for stochastic integrals. A general case of vector semimartingales not necessarily continuous is considered. The second order derivatives arise naturally after integration by parts and because of connections of local times with quadratic characteristics. In turn, Tanaka's formula was deduced by the author earlier [in: Séminaire de probabilités XXX. Lect. Notes Math. 1626, 261-287 (1996; Zbl 0870.60050)] without using of Itô's one.