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.
Bibliographical noteFunding Information:
The author was partially supported by NSF Grant DMS-1160569.
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- Hörmander's theorem