Regularity structure in stochastic PDE

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

메타데이터

위키데이터

• ID : Q28401890