SG(2,3)上的布朗运动

Brownian Motion on SG(2, 3)

研究了分形集SG（2，3）上随机游动转移概率及首中时的性质，结合分枝过程理论构造了SG（2，3）上的布朗运动，并研究了这种过程半群的对称的性质以及样本轨道的性质，证明了其样本轨道以概率1具有指数log3／log（90/17）的Hoder连续性．此外，对过程的首中时也进行了讨论，并得到了首中时的分布函数及矩的估计．

In this paper, we first discuss transition probability and hitting time of the simple random walk on the fractal SG(2,3), and combined with branch processes theory, We construct a Feller process X on SG (2, 3), and prove that the semigroup of X is symmetric respect to some radon measure, and the sample paths are holder contlnuous with the order log3/log(17)in probabllity one. further more, the hitting time are also discussed, an estimate for the distribution function and moment of hitting time is given.