广义分数布朗运动的若干性质

Some Properties of a Generalized Fractional Brownian Motion

摘要: 本文, 我们定义了一类新的分数布朗运动, 研究了它的局部非决定性和局部时的联合连续性, 最后给出了它的水平集的Hausdorff维数的上、下界.

Abstract: In the paper, we give a new generalization of fraction Brownian motion (gfBm). We study the existence of the local nondeterminism and the joint continuity of the local time of gfBm, and we get upper and lower bounds of Hausdorff dimensions of the level sets of a gfBm.