Skip to Main content Skip to Navigation
Theses

Singular KPZ Type Equations

Abstract : In this thesis, we investigate the existence and the uniqueness of the solution of the generalised KPZ equation. We use the recent theory of regularity structures inspired from the rough path and introduced by Martin Hairer in order to give a meaning to this singular equation. The procedure contains an algebraic part through the renormalisation group and a stochastic part with the computation of renormalised stochastic processes. One major improvement in the theory of the regularity structures is the definition of the renormalisation group using a Hopf algebra on some labelled trees. This new construction paves the way to simple formulas very useful for the renormalised stochastic processes. Then the convergence is obtained by an efficient treatment of some Feynman diagrams.
Document type :
Theses
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-01306427
Contributor : Yvain Bruned <>
Submitted on : Saturday, April 23, 2016 - 6:13:39 PM
Last modification on : Thursday, March 26, 2020 - 9:14:35 PM
Long-term archiving on: : Sunday, July 24, 2016 - 10:30:14 AM

Identifiers

  • HAL Id : tel-01306427, version 1

Citation

Yvain Bruned. Singular KPZ Type Equations. Mathematics [math]. Paris 6, 2015. English. ⟨tel-01306427v1⟩

Share

Metrics

Record views

145

Files downloads

18