$G$-Gaussian random fields and stochastic quantization under nonlinear expectation

Haoran Hu

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arXiv · 2307.10942

$G$-Gaussian random fields and stochastic quantization under nonlinear expectation

Haoran Hu

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Abstract

We investigate the application of Parisi-Wu stochastic quantization to the construction of random fields within the sublinear expectation framework. Using the semigroup approach and the infinite dimensional $G$-Ornstein Uhlenbeck process, we derive the unique mild solution to the robust Langevin dynamics of bosonic free field -- a parabolic linear stochastic partial differential equation (SPDE) driven by cylindrical $G$-Brownian motions. Mimicking the linear expectation case, we show the equilibrium distribution of the mild solution is the sublinear expectation analog of the massive Gaussian free field.

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Haoran Hu. 2024-12-13. $G$-Gaussian random fields and stochastic quantization under nonlinear expectation. https://arxiv.org/abs/2307.10942

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