Hörmander’s theorem for stochastic partial differential equations
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- by N. V. Krylov
- St. Petersburg Math. J. 27 (2016), 461-479
- DOI: https://doi.org/10.1090/spmj/1398
- Published electronically: March 30, 2016
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Abstract:
Hörmander’s type hypoellipticity theorem for stochastic partial differential equations is proved in the case where the coefficients are only measurable with respect to the time variable. Such equations arise, for instance, in filtering theory of partially observable diffusion processes. If one sets all coefficients of the stochastic part to be zero, one gets new results for usual parabolic PDEs.References
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Bibliographic Information
- N. V. Krylov
- Affiliation: 127 Vincent Hall, University of Minnesota, Minneapolis, Minnesota 55455
- MR Author ID: 189683
- Email: krylov@math.umn.edu
- Received by editor(s): October 20, 2014
- Published electronically: March 30, 2016
- Additional Notes: The author was partially supported by NSF Grant DMS-1160569
- © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 27 (2016), 461-479
- MSC (2010): Primary 35R40
- DOI: https://doi.org/10.1090/spmj/1398
- MathSciNet review: 3570961
Dedicated: Dedicated to N. N. Ural’tseva on her jubilee