An It\=o formula in the space of tempered distributions
Abstract
We extend the It\=o formula 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.
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