A stochastic transport linear equation (STLE) with multiplicative space-time dependent noise is studied. It is shown that, under suitable assumptions on the noise, a multiplicative renormalization leads to convergence of the solutions of STLE to the solution of a deterministic parabolic equation. Existence and uniqueness for STLE are also discussed. Our method works in dimension \(d\ge 2\); the case \(d=1\) is also investigated but no conclusive answer is obtained.

中文翻译：

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关于随机运输方程到确定抛物线方程的收敛性

研究了具有与时空相关的可乘噪声的随机运输线性方程（STLE）。结果表明，在适当的噪声假设下，乘法重归一化导致STLE的解收敛到确定性抛物方程的解。还讨论了STLE的存在性和唯一性。我们的方法适用于维度\（d \ ge 2 \） ; 也调查了\（d = 1 \）的情况，但没有得出确定的答案。