zbMATH — the first resource for mathematics

The estimation of the Hausdorff dimension for \(\mu\)-statistically self-affine sets. (Chinese) Zbl 0979.28002
The authors introduce a class of fractals, called \(\mu\)-statistically self-affine sets. Included as subclasses of \(\mu\)-statistically self-affine fractals are Falconer’s self-affine fractals [K. J. Falconer, “The Hausdorff dimension of self-affine fractals”, Math. Proc. Camb. Philos. Soc. 103, No. 2, 339-350 (1988; Zbl 0642.28005)] and Graf’s statistically self-similar fractals [S. Graf, “Statistically self-similar fractals”, Probab. Theory Relat. Fields 74, 357-392 (1987; Zbl 0591.60005)]. The authors also give an upper bound and a lower bound for the Hausdorff dimension of \(\mu\)-statistically self-affine fractals.
28A80 Fractals
60G46 Martingales and classical analysis