两指标布朗球的构造及相关概率估计

The Construction of Two-Parameters Brownian Sphere and Related Probability Estimations

利用三维布朗运动和带参数指标的均匀分布构造了两指标布朗球模型.根据其构造原理,探讨了该类随机球模型的相关几何性质,给出了其对应表面积与体积的数字特征.特别的,借助该随机球讨论了具有收胀特征的类分子模型的留守及碰撞问题,并给出了其相应概率估计.

In this paper,a two-parameters Brownian sphere model is constructed by using three-dimensional Brownian motions and uniform distribution with parameter index.According to its construction principle,we discuss the related geometric properties of this kind of random sphere model,and give the numerical characteristics of its corresponding surface area and volume.Specifically,the sojourn and collision problems of class molecular models with swelling characteristics were discussed using this random ball,and corresponding probability estimates were provided.