Another look into the Wong-Zakai Theorem for Stochastic Heat Equation

@article{Gu2018AnotherLI,
  title={Another look into the Wong-Zakai Theorem for Stochastic Heat Equation},
  author={Y. Gu and Li-Cheng Tsai},
  journal={arXiv: Probability},
  year={2018}
}
  • Y. Gu, Li-Cheng Tsai
  • Published 2018
  • Mathematics, Physics
  • arXiv: Probability
  • Consider the heat equation driven by a smooth, Gaussian random potential: \begin{align*} \partial_t u_{\varepsilon}=\tfrac12\Delta u_{\varepsilon}+u_{\varepsilon}(\xi_{\varepsilon}-c_{\varepsilon}), \ \ t>0, x\in\mathbb{R}, \end{align*} where $\xi_{\varepsilon}$ converges to a spacetime white noise, and $c_{\varepsilon} $ is a diverging constant chosen properly. For any $ n\geq 1 $, we prove that $ u_{\varepsilon} $ converges in $ L^n $ to the solution of the stochastic heat equation. Our… CONTINUE READING
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