"Regularity structure in stochastic PDE"의 두 판 사이의 차이
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imported>Pythagoras0 (section 'expositions' updated) |
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==introduction== | ==introduction== | ||
| + | * These lecture notes grew out of a series of lectures given by the second named author in short courses in Toulouse, Matsumoto, and Darmstadt. | ||
| + | * The main aim is to explain some aspects of the theory of "Regularity structures" developed recently by Hairer in arXiv:1303.5113 . | ||
| + | * This theory gives a way to study well-posedness for a class of stochastic PDEs that could not be treated previously. | ||
| + | * Prominent examples include the KPZ equation as well as the dynamic $\Phi^4_3$ model. Such equations can be expanded into formal perturbative expansions. | ||
| + | * Roughly speaking the theory of regularity structures provides a way to truncate this expansion after finitely many terms and to solve a fixed point problem for the "remainder". | ||
| + | * The key ingredient is a new notion of "regularity" which is based on the terms of this expansion. | ||
| + | |||
==expositions== | ==expositions== | ||
2016년 6월 8일 (수) 21:42 판
introduction
- These lecture notes grew out of a series of lectures given by the second named author in short courses in Toulouse, Matsumoto, and Darmstadt.
- The main aim is to explain some aspects of the theory of "Regularity structures" developed recently by Hairer in arXiv:1303.5113 .
- This theory gives a way to study well-posedness for a class of stochastic PDEs that could not be treated previously.
- Prominent examples include the KPZ equation as well as the dynamic $\Phi^4_3$ model. Such equations can be expanded into formal perturbative expansions.
- Roughly speaking the theory of regularity structures provides a way to truncate this expansion after finitely many terms and to solve a fixed point problem for the "remainder".
- The key ingredient is a new notion of "regularity" which is based on the terms of this expansion.
expositions
- Ajay Chandra, Hendrik Weber, Stochastic PDEs, Regularity Structures, and Interacting Particle Systems, arXiv:1508.03616 [math.AP], August 14 2015, http://arxiv.org/abs/1508.03616
- Martin Hairer, The motion of a random string, arXiv:1605.02192 [math.PR], May 07 2016, http://arxiv.org/abs/1605.02192