We analyze the solution to the stochastic Burgers equation with additive space-time white noise. We show that this solution can be expressed as a sum of a random field that solves the stochastic heat equation with additive space-time white noise and a more regular random field. We apply these results in order to estimate the drift parameter of solution to the Burgers equation by exploiting the behavior of the p-variations of the solution in time and in space.

中文翻译：

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随机Burgers方程的路径分析和参数估计

我们分析了具有加性时空白噪声的随机Burgers方程的解。我们表明，该解决方案可以表示为随机场的总和，该随机场解决具有加性时空白噪声和更规则的随机场的随机热方程。我们利用这些结果，以通过利用解的p-变量在时间和空间上的行为来估计Burgers方程的解的漂移参数。