N指标d维广义Wiener过程的图集和水平集的Hausdorff和Packing维数

HAUSDORFF AND PACKING DIMENSIONS OF GRAPH AND LEVEL SETS FOR N PARAMETER d DIMENSIONAL GENERALIZED WIENER PROCESS

研究了张润楚引进的Ｎ指标ｄ维广义Ｗｉｅｎｅｒ过程的样本轨道的分形性质，得到了图集和水平集的Ｈａｕｓｄｏｒｆｆ维数及Ｐａｃｋｉｎｇ维数．此结果包含并推广了ＢｒｏｗｎＳｈｅｅｔ的结果．

Fractal properties of sample path of N parameter d dimensionial generalized Wiener processes are studied. The Hausdorff and Packing dimensions of graph Gr| F and level set -1 (x)∩F for any compact set F in R N + 0} are obtained. These results contains and extends the results of Brown Sheet.