$G$-Gaussian random fields and stochastic quantization under nonlinear expectation
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913610037460992 |
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| author | Hu, Haoran |
| author_facet | Hu, Haoran |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10942 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $G$-Gaussian random fields and stochastic quantization under nonlinear expectation Hu, Haoran Probability Mathematical Physics 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. |
| title | $G$-Gaussian random fields and stochastic quantization under nonlinear expectation |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2307.10942 |