Old problems of the mathematical description of the economical behavior of a man are briefly reviewed. They are the comparison of choices of a man between uncertain and sure games and the radically different behavior of a man in different domains. The proposed solution of the problems consists...

A brief introduction to the eventology, which has originated recently as a new line of probability theory. This line studies eventological motion of random-fuzzy events (eventological motion of events motion of matter or motion of mind changing the eventological distributions), introduces the...

The article raises the question of possible existence of ruptures, gaps in the probability scale which are caused by noises, uncertainties. A hypothesis of existence of such ruptures may be used to solve a number of problems of, e.g., utility theory in economics. The calculations give the...

The two main goals of the present article are: 1) To prove an existence theorem for forbidden zones for the expectations of real-valued random variables. 2) To define transformations (named here as auto-transformations) of the probability density functions (PDFs) of random variables into similar...

Suppose a random variable takes on values in an interval. The minimal distance between the expectation of the variable and the nearest boundary of the interval is considered in the present article. A question whether this distance can be neglected with respect to the standard deviation is...

A forbidden zones theorem is deduced in the present article. Its consequences and applications are preliminary considered. The following statement is proven: if some non-zero lower bound exists for the variance of a random variable, that takes on values in a finite interval, then non-zero bounds...

The business cycles are generated by the oscillating macro-/micro-/nano- economic output variables in the economy of the scale and the scope in the amplitude/frequency/phase/time domains in the economics. The accurate forward looking assumptions on the business cycles oscillation dynamics can...

A forbidden zones theorem is proven in the present article. If some non-zero lower bound exists for the variance of a random variable, whose support is located in a finite interval, then non-zero bounds or forbidden zones exist for its expectation near the boundaries of the interval. The article...

A systematic introduction to sub-interval images (or SI-images or S-IIs) is presented here. General outlook of possible use of the SI-analysis for Big Data is given. Basic notions of S-IIs are formulated including cuboids of gravity and sub-interval copies of databases. Two concepts of...

A forbidden zones theorem, mathematical approach and model are proposed in the present article. In particular, the approach supposes that people decide as if there were some biases of the expectations of measurement data. The article is motivated by the need of a theoretical support for the...