The Annals of Probability

Strong solutions to the stochastic quantization equations

Giuseppe Da Prato and Arnaud Debussche

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We prove the existence and uniqueness of a strong solution of the stochastic quantization equation in dimension 2 for almost all initial data with respect to the invariant measure. The method is based on a fixed point result in suitable Besov spaces.

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Ann. Probab., Volume 31, Number 4 (2003), 1900-1916.

First available in Project Euclid: 12 November 2003

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Primary: 81S20: Stochastic quantization 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 42B99: None of the above, but in this section

Stochastic quantization Gibbs measures Besov spaces pathwise solutions


Da Prato, Giuseppe; Debussche, Arnaud. Strong solutions to the stochastic quantization equations. Ann. Probab. 31 (2003), no. 4, 1900--1916. doi:10.1214/aop/1068646370.

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