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An Itō Formula in the Space of Tempered Distributions

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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.

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  • 01 November 2017

    The following corrections are required in Theorem 4.7.

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Acknowledgments

The author would like to thank Professor B. Rajeev, Indian Statistical Institute, Bangalore, for valuable suggestions during the work and pointing out the way to Theorem 4.5.

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  1. Indian Statistical Institute Bangalore Centre, Bangalore, India

    Suprio Bhar

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  1. Suprio Bhar
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Correspondence to Suprio Bhar.

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A correction to this article is available online at https://doi.org/10.1007/s10959-017-0792-y.

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Bhar, S. An Itō Formula in the Space of Tempered Distributions. J Theor Probab 30, 510–528 (2017). https://doi.org/10.1007/s10959-015-0639-3

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