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arXiv:1502.00157math.PR

Lectures on singular stochastic PDEs

M. Gubinelli, N. Perkowski

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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.

arXiv comments
73 pages, 4 figures
Journal reference
Ensaios Mat. Vol. 29, 2015
DOI
Subjects
math.PRProbability

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  1. TeXmacs and the Art of Mathematical Writing 1 comment

    • I generally use TeXmacs for notes, derivations, lectures, articles, all, of course. Most of my papers in the last 7 years, around 15 and all my lectures in the same period, circa 2 courses a year. More in detail, all these papers are been written completely in TeXmacs and then…

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