Lectures on singular stochastic PDEs
By Massimiliano Gubinelli. Ensaios matemáticos, 2015
54 citations recorded by the source corpus.
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 [GJ10, GJ13] and that of paracontrolled distributions, recently introduced in [GIP13]. In order to maintain a link with physical intuitions, we motivate such singular SPDEs via a homogenization result for a di usion in a random potential.
Subfields: Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/609102ff38d846db7b0621a8765ce255a28a8372
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In Finance
- Samy Tindel
- Massimiliano Gubinelli
- A. Deya
- Nicolas Perkowski
- Martina Hofmanov'a
- Martin Hairer
- Peter K. Friz
- David Nualart
In Mathematical Physics
- Samy Tindel
- Massimiliano Gubinelli
- Nicolas Perkowski
- A. Deya
- Martina Hofmanov'a
- Martin Hairer
- Hendrik Weber
- Jean-Christophe Mourrat
Citations in the corpus
- A priori estimates for rough PDEs with application to rough conservation laws (2016, background): “A more conservative approach, useful in many situations but not as general, is the paracontrolled calculus developed by Gubinelli, Imkeller and Perkowski [31,32].”
- Energy solutions of KPZ are unique (2015, background): “ At(ϕ) = Z t 0 ∂xu 2 s(ϕ)ds. almost surely for all t∈ [0,T] and ϕ∈ S. Existence of energy solutions of SBE can be proved via Galerkin approximations or approximation of the non–linear term as done in [4, 5]. The aim of this note is to show that energy solutions of SBE are in fact adapted to the nois”