An It\=o formula in the space of tempered distributions

We extend the It=o formula \cite{MR1837298}*{Theorem 2.3} for semimartingales with rcll paths. We also comment on Local time process of such semimartingales. We apply the It=o formula to L'evy processes to obtain existence of solutions to certain classes of stochastic differential equations in the Hermite-Sobolev spaces.