An Itō formula in the space of tempered distributions
arXiv:1411.6145 · doi:10.1007/s10959-015-0639-3
Abstract
We extend the Itō formula \cite{MR1837298}*{Theorem 2.3} for semimartingales with rcll paths. We also comment on Local time process of such semimartingales. We apply the Itō formula to Lévy processes to obtain existence of solutions to certain classes of stochastic differential equations in the Hermite-Sobolev spaces.