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

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 徐赐文 Xu Ciwen 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 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. 广义Wiener过程 图集 水平集 Hausdorff维数 Packing维数 generalized Wiener process graph level set Hausdorff dimension Packing dimension O211.6 国家自然科学基金,国家教委博士点专项基金 1998-01-01 2021-04-01 1