Some recent progress in singular stochastic partial differential equations
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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.References
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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 - © Copyright 2019 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 57 (2020), 409-454
- DOI: https://doi.org/10.1090/bull/1670
- MathSciNet review: 4108091