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An Itō Formula in the Space of Tempered Distributions

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  • Suprio Bhar

    (Indian Statistical Institute Bangalore Centre)

Abstract

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.

Suggested Citation

  • Suprio Bhar, 2017. "An Itō Formula in the Space of Tempered Distributions," Journal of Theoretical Probability, Springer, vol. 30(2), pages 510-528, June.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:2:d:10.1007_s10959-015-0639-3
    DOI: 10.1007/s10959-015-0639-3
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    References listed on IDEAS

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    1. B. Rajeev, 2013. "Translation invariant diffusions in the space of tempered distributions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(2), pages 231-258, April.
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