Some recent progress in singular stochastic partial differential equations

Corwin, Ivan; Shen, Hao

doi:10.1090/bull/1670

Some recent progress in singular stochastic partial differential equations
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Bull. Amer. Math. Soc. 57 (2020), 409-454 Request permission

Abstract:

Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many such equations are too singular to admit classical treatment. In this article we review some recent progress in defining, approximating, and studying the properties of a few examples of such equations. We focus mainly on the dynamical $\Phi ^4$ equation, the KPZ equation, and the parabolic Anderson model, as well as a few other equations which arise mainly in physics.

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Additional Information

Ivan Corwin
Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
MR Author ID: 833613
Email: corwin@math.columbia.edu
Hao Shen
Affiliation: Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Drive, Madison, Wisconsin 53706
MR Author ID: 1041376
Email: pkushenhao@gmail.com
Received by editor(s): April 8, 2019
Published electronically: September 26, 2019
Additional Notes: The first author was partially supported by the Packard Fellowship for Science and Engineering, and by the NSF through DMS-1811143 and DMS-1664650
The second author was partially supported by the NSF through DMS-1712684 and DMS-1909525
Journal: Bull. Amer. Math. Soc. 57 (2020), 409-454
DOI: https://doi.org/10.1090/bull/1670
MathSciNet review: 4108091