Hörmander's theorem for stochastic partial differential equations

N. V. Krylov

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)461-479
Number of pages19
JournalSt. Petersburg Mathematical Journal
Issue number3
StatePublished - 2016

Bibliographical note

Funding Information:
The author was partially supported by NSF Grant DMS-1160569.

Copyright 2016 Elsevier B.V., All rights reserved.


  • Hypoellipticity
  • Hörmander's theorem
  • Spdes


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