A symbolic dynamics approach to random walk on Koch fractal (Part II)

A new symbolic dynamic approach is applied to the research of the random walk and Brownian motion (BM) on Koch fractal. Base on the arithmetic analytic expression of Koch curve We give some accurate formulas of the random walk including, the muscle-shaped G-density in Gauss process, and the comb-shaped probability distribution of echo classes on the basis of the symbolic description of the echo classes, and then constitute the BM in terms of Hausdorff measure, discuss particularly the relationship between the chemical distance and the Hausdorff measure. Finally, the Wiener process in terms of Hausdorff measure is parallel constructed.