随机分形

本文概括了随机分形的主要结果，综述了随机分形的最新进展和目前的动态，提出了一些末解决的问题，全文共分为三部分：（１）由随机过程和随机场（如Ｌｅｖｙ过程，Ｇａｕｓｓ场，自相似过程等）产生的各种随机分形集（如象集、水平集、Ｋ重点集等）的Ｈａｕｓｄｏｒｆｆ维数、测度和ｐａｃｋｉｎｇ维数、测试；（２）随机Ｃａｎｔｏｒ型集和统计自相似集的维数和测试；（３）分形集（如Ｓｐｉｅｒｐｉｎｓｋｉ ｇａｓｋｅｔ，ｎｅ

Random Fractals

This paper gives a comprehensive survey of the studies of random fractals con-cerning principal results,recent progresses and up-to-date trends,and proposes some open prob-lems.It explains, as appearing from stochastic processes(e.g.Levy proceses,Gaussian fields)(1)the Harsdorff as well as the packing dimensions and measure functions of various randomfractal sets(e.g.image set,level set);(2) the dimensions and measure functions of the randomfractal sets of Cantor type and of the statistical self-similar sets. It also provides(3)the con-structions and properties of the stochastic processes on fractal sets(e.g.Sierpinski gasket,nestfractal).