Lectures on singular stochastic PDEs

M. Gubinelli and N. Perkowski

First issued 31 January 2015 · PDF

Abstract

These are the notes for a course at the 18th Brazilian School of Probability held from August 3rd to 9th, 2014 in Mambucaba. The aim of the course is to introduce the basic problems of non–linear PDEs with stochastic and irregular terms. We explain how it is possible to handle them using two main techniques: the notion of energy solutions and that of paracontrolled distributions. In order to maintain a link with physical intuitions, we motivate such singular SPDEs via a homogenisation result for a diffusion in a random potential.

Versions

1. Version 3 (arXiv v2) current
   29 July 2017
   arXiv comments: 73 pages, 4 figures
   PDF · LaTeX source · files and digests · arXiv:1502.00157
2. Version 2 (arXiv v1)
   31 January 2015
   arXiv comments: 67 pages, 4 figures
   PDF · LaTeX source · files and digests · arXiv:1502.00157
3. Version 1
   written 29 January 2015, not public at the time
   PDF · TeXmacs source · files and digests

Cite

M. Gubinelli and N. Perkowski. Lectures on singular stochastic PDEs. Papers of Massimiliano Gubinelli, 2015, version 3. https://mgubi.org/papers/paper/singular-spde-lectures/

Licence: arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors

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