The Annals of Probability

Paracontrolled distributions and the 3-dimensional stochastic quantization equation

Rémi Catellier and Khalil Chouk

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aop/1535097636

Digital Object Identifier
doi:10.1214/17-AOP1235

Mathematical Reviews number (MathSciNet)
MR3846835

Zentralblatt MATH identifier
06964345

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

Keywords
Singular SPDEs paracontrolled calculus

Citation

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. https://projecteuclid.org/euclid.aop/1535097636


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References

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