The Annals of Probability

Paracontrolled distributions and the 3-dimensional stochastic quantization equation

Rémi Catellier and Khalil Chouk

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We prove the existence and uniqueness of a local in time solution to the periodic $\Phi^{4}_{3}$ model of stochastic quantisation using the method of paracontrolled distributions introduced recently by M. Gubinelli, P. Imkeller and N. Perkowski in [Forum Math., Pi 3 (2015) e6].

Article information

Ann. Probab., Volume 46, Number 5 (2018), 2621-2679.

Received: November 2013
Revised: April 2017
First available in Project Euclid: 24 August 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60H40: White noise theory
Secondary: 42B25: Maximal functions, Littlewood-Paley theory

Singular SPDEs paracontrolled calculus


Catellier, Rémi; Chouk, Khalil. Paracontrolled distributions and the 3-dimensional stochastic quantization equation. Ann. Probab. 46 (2018), no. 5, 2621--2679. doi:10.1214/17-AOP1235.

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