论文标题
关于最大布朗片的分布，仅限于较低维度
On the distribution of maximum of a Brownian sheet restricted to a lower-dimensional set
论文作者
论文摘要
我们获得具有特殊协方差函数的高斯随机场随机等效性的足够条件。这些结果将DOOB的转换（高斯和维纳过程的随机等效性的条件）推广到随机场的情况（高斯过程的随机等效性和布朗尼纸的情况）。我们看一下在比磁场尺寸低的尺寸的布朗纸上找到至高无上的问题的问题。我们考虑具有一定漂移的布朗薄板的概率以达到零水平。获得的结果可以大大简化布朗板功能分布的问题，从而将其简化为在平行教的问题的问题，该问题的尺寸低于田间的尺寸。我们考虑通过对相应的字段进行建模并将经验概率与理论概率进行比较来验证所获得定理的有效性的示例。
We obtain sufficient conditions of stochastic equivalence of Gaussian random fields with special covariance function. These results generalize Doob's transformation (condition of stochastic equivalence of a Gaussian and a Wiener processes) to the case of random fields (condition of stochastic equivalence of a Gaussian process and a Brownian sheet). We look at the problem of finding the distribution of supremum of a Brownian sheet on a set with a dimension lower than the dimension of the field. We consider the probability of a Brownian sheet with a certain drift to attain zero level. The obtained results can significantly simplify the problem of finding distributions of functionals of a Brownian sheet by reducing it to the problem of finding distributions on parallelepipeds with dimension lower than the dimension of the field. We consider examples that verify validity of the obtained theorem by modeling corresponding fields and comparing empirical probabilities with theoretical ones.
