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SSS 01
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Sigma Series
in Stochastics
SSS Volume 1
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Sigma Series in Stochastics, Volume 1, 147--174
Heldermann Verlag 2004
Theoretical Stochastics
Elart von Collani
University of Würzburg, Sanderring 2, 97070 Würzburg, Germany
Stochastics as an independent branch of natural science can be
based neither on probability theory nor on statistics, but needs its own
theoretical fundaments. These are developed in the present paper.
Uncertainty refers to the change from past to future and, therefore,
variables are necessary describing the determinate past and
the indeterminate future development. Moreover, functions are needed
which model the range of variability and the structure of variability and thus
the laws of change. The paper introduces the necessary quantities and
develops generic representations for them. Moreover, classifying
the structure of randomness leads to the definition of disjoint families
of probability distributions allowing to assign an appropriate type of
probability distribution to a given random variable with
known qualitative behavior.
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