An Itō Formula in the Space of Tempered Distributions
Journal of Theoretical Probability
We extend the Itō formula (Rajeev in From Tanaka’s formula to Ito’s formula: distributions, tensor products and local times, Springer, Berlin, 2001, Theorem 2.3) for semimartingales with paths that are right continuous and have left limits. We also comment on the 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.
Bhar, Suprio, "An Itō Formula in the Space of Tempered Distributions" (2017). Journal Articles. 2567.