Hörmander's theorem for stochastic partial differential equations

N. V. Krylov

doi:10.1090/spmj/1398

Hörmander's theorem for stochastic partial differential equations

N. V. Krylov

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	461-479
Number of pages	19
Journal	St. Petersburg Mathematical Journal
Volume	27
Issue number	3
DOIs	https://doi.org/10.1090/spmj/1398
State	Published - 2016

Bibliographical note

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

Keywords

Hypoellipticity
Hörmander's theorem
Spdes

Access

10.1090/spmj/1398

OpenUrl availability

Full text

Cite this

@article{eb015b226e9741299549f542e8c21a58,

title = "H{\"o}rmander's theorem for stochastic partial differential equations",

abstract = "H{\"o}rmander'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.",

keywords = "Hypoellipticity, H{\"o}rmander's theorem, Spdes",

author = "Krylov, {N. V.}",

note = "Funding Information: The author was partially supported by NSF Grant DMS-1160569.",

year = "2016",

doi = "10.1090/spmj/1398",

language = "English (US)",

volume = "27",

pages = "461--479",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "3",

}

TY - JOUR

T1 - Hörmander's theorem for stochastic partial differential equations

AU - Krylov, N. V.

N1 - Funding Information: The author was partially supported by NSF Grant DMS-1160569.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Hypoellipticity

KW - Hörmander's theorem

KW - Spdes

UR - http://www.scopus.com/inward/record.url?scp=84963576867&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963576867&partnerID=8YFLogxK

U2 - 10.1090/spmj/1398

DO - 10.1090/spmj/1398

M3 - Article

AN - SCOPUS:84963576867

SN - 1061-0022

VL - 27

SP - 461

EP - 479

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

IS - 3

ER -

Hörmander's theorem for stochastic partial differential equations

Abstract

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this