Probability Space of Stochastic Fractals

Abstract

We develop a general method for the construction of a probability structure on the space ᑟ of random sets in R. For this purpose, by using the introduced notion of c-system, we prove a theorem on the unique extension of a finite measure from a c-system to the minimal c-algebra. The obtained structure of measurability enables one to determine probability distributions of the c-algebra of random events sufficient, e.g., for the so-called fractal dimensionality of random realizations to be considered as a measurable functional on ᑟ.

Use of Neural Networks for Identification of Artifacts in Electroencephalographic Signals Decomposed Using Wavelet Packet Transform

“…The probabilistic description of such ran dom fractals was given in [9]. The probability p = 1 of fractal non random Hausdorff dimension was reported in [10,11].…”