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Article Dans Une Revue Communications in Contemporary Mathematics Année : 2022

A Microlocal Approach to Renormalization in Stochastic PDEs

Nicolò Drago
  • Fonction : Auteur
Paolo Rinaldi
  • Fonction : Auteur

Résumé

We present a novel framework for the study of a large class of non-linear stochastic PDEs, which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use techniques proper of microlocal analysis which allow us to discuss renormalization and its associated freedomw without resorting to any regularization scheme and to the subtraction of infinities. As an example of the effectiveness of the approach we apply it to the perturbative analysis of the stochastic $\Phi^3_d$ model.

Dates et versions

hal-02955071 , version 1 (01-10-2020)

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Claudio Dappiaggi, Nicolò Drago, Paolo Rinaldi, Lorenzo Zambotti. A Microlocal Approach to Renormalization in Stochastic PDEs. Communications in Contemporary Mathematics, 2022, 24 (07), ⟨10.1142/S0219199721500759⟩. ⟨hal-02955071⟩
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