Remaking the primary source of an old good idea of the “lattice expectation”, published by me in 1975 at the first time and subsequently, especially in the western literature on stochastic geometry and the theory of random sets, named from a light hand of Dietrich Stoyan [1994] “Vorob’ev...

The paper introduces new notion for the set-valued mean set of a random set. The means are defined as families of sets that minimize mean distances to the random set. The distances are determined by metrics in spaces of sets or by suitable generalizations. Some examples illustrate the use of the...

Eventologically multivariate extensions of probability theory’s limit theorems are proposed. Eventologically multivariate version of limit theorems extends its classical probabilistic interpretation and involves into its structure of dependencies of arbitrary set of events which appears in...

The eventological theory of decision-making, the theory of event-based decision-making is a theory of decision-making based on eventological principles and using results of mathematical eventology [1]; a theoretical basis of the practical eventology [2, 3, 4]. The beginnings of this theory which...

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...

A new approach to portfolio analysis of financial market risks by random set tools is considered. Despite many attempts, the consistent and global modeling of financial markets remains an open problem. In particular it remains a challenge to find a simple and tractable economic and probabilistic...

This article brings in two new discrete distributions: multivariate Binomial distribution and multivariate Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson distributions. Accordingly to eventology new laws take into...

Totals of the eventological safety system modeling is considered for examples and illustrations, which are intended to demonstrate the main features of the algorithm for calculating the risk of a dangerous event at the company under established the event-related circumstances based on the...

In this paper, we present an eventological model of a mean probability event for a set of events. This model is analogous to the notion of a mean measure set

Many-events-based and many-agent eventological models of supply and demand are offered. In thesemodels new concepts of equilibrium intervals of prices and subsets of goods are introduced for the firsttime. These models follow from the eventological H-theorem (eventological generalization of...