广义布朗单的容度估计

Capacity Estimates for Generalized Brownian Sheet

研究了既没有平稳增量性,也没有scaling性质的N指标d维广义布朗单的容度问题．证明了广义布朗单“好象”一个局部平稳增量过程,应用Cairoli极大不等式和多参数鞅的方法得到了广义布朗单的碰撞概率与容度之间的关系,给出了其碰撞概率的确切容度估计．所得结果包含了布朗单和可加布朗运动的相应结果．

The problem of the capacity for N-parameter d-dimensional generalized Brownian sheet, which may satisfy neither scaling property nor stationary increments, is investigated. It is proved that the generalized Brownian sheet locally looks like a stationary process. The relationship between the hitting probabilities for generalized Brownian sheet and the capacity is obtained by means of Cairoli＇s maximal inequality and multiparameter martingales. An explicit capacity estimate for its hitting probabilities is provided. The conclusions about the Brownian sheet and the additive Brownian motion can be considered as special cases of our results.