Abstract
Self-similarity of systems is very popular and intensively developing field during last decades. To this field belong so-called stable distributions and their generalization. In Klebanov and Slámová (2014) there was given an approach to define additive systems with the property of random self-similarity - casual stability (c.s.). Here we continue study the notion of casual stability for additive systems of random variables (r.v.). We also give a modification of this definition and spread them on multiplicative systems of r.v. and on the system with operations of taking minimum or maximum of r.v. The case of systems with a random number of elements is also considered.
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