On the description of stochastic systems

Abstract

A set-up of the systemic description of a (stochastic) system, particular states of which form (on the lowest determination level of the system state) a population of random events, is presented. Elementary and hierarchic stochastic systems are considered and the structure of their description is formulated. As an application of the conception, the set-up of the description of liquid media motion is considered. The generic notion of the description of any object (or phenomenon) behaving stochastically is a random event. The randomness of an event expresses its systemic property revealed in a population of events, each of which could have happened instead of the given event under the same conditions, specified as the object's state fixed in terms reflecting the quality of the object as an entirety. The object, particular states of which are random events, is further called a stochastic system. There are two different levels of presentation of the state of a stochastic system - the level of a stochastic system as an entirety and the level of a random event. The state of a stochastic system as an entirety organizes the population of random events by providing the population with a probability distribution. A population, characterized by a probability distribution, is called a statistical ensemble. The properties of a statistical ensemble as well as of the probability distribution are reflected by the system quality as an entirety. Particular descriptions of a stochastic system, formulated in terms characterizing the system as an entirety, its particular states, and organization of its particular states as random events expressed by the probability distribution, form the subject of systemic description. The systemic description treats a stochastic system from the point of view of all its particular descriptions and links connecting the particular descriptions.