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Hörmander's theorem for stochastic partial differential equations


Author: N. V. Krylov
Original publication: Algebra i Analiz, tom 27 (2015), nomer 3.
Journal: St. Petersburg Math. J. 27 (2016), 461-479
MSC (2010): Primary 35R40
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.


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Additional Information

N. V. Krylov
Affiliation: 127 Vincent Hall, University of Minnesota, Minneapolis, Minnesota 55455
Email: krylov@math.umn.edu

DOI: https://doi.org/10.1090/spmj/1398
Keywords: Hypoellipticity, SPDEs, H\"ormander's theorem
Received by editor(s): October 20, 2014
Published electronically: March 30, 2016
Additional Notes: The author was partially supported by NSF Grant DMS-1160569
Dedicated: Dedicated to N. N. Ural’tseva on her jubilee
Article copyright: © Copyright 2016 American Mathematical Society