International Encyclopedia of Systems and Cybernetics

The concept of random process is somewhat obscured due to the fact that the role of time (past, present, future) is generally not well understood.

P. VENDRYES states: "As an experimental example one can take the throw of a dice. This is a random process… It is datum of common experience that the throwing of a dice occurs in two stages. During the first stage the player makes a choice (a bet) of one of the six faces of the dice. These are therefore six simultaneous alternatives available to the player. This multiplicity of alternatives makes the process indeterminate and unpredictable. The second phase occurs when anyone of the six faces turns up, so excluding the other five. This exclusion makes it an irreversible process. Thus, there are three attributes of a perfect random process: multiplicity, unpredictability and irreversibility.

"The random process distinguishes itself from the deterministic process during the first stage by the multiplicity of Simultaneously possible outcomes. Each of these cases has a certain probability of turning up. The probability belongs to the first stage of the random process, before its realization; it is virtual because the second stage has not yet taken place; it is oriented towards an unpredictable future, and it is transient because it disappears as soon as the second stage takes place." (1989, p.14)

VENDRYES' concept is clearly related to Bayesian subjective probabilities.

From another viewpoint, R.V. JENSEN writes: "Attempts to reconcile the probabilistic laws of statistical mechanics give birth to a new branch of mathematics, called ergodic theory, which provides a means of classifying different deterministic dynamical systems with irregular behavior. In particular, this classification scheme defines symptoms for a hierarchy of different classes of random behavior, "statistical diseases" of increasing severity" (1987, p.176).

Ergodic systems allow for randomness within a general determinism. Further along, chaotic systems seem completely random, but still possess an underlying determinism. It becomes thus necessary to consider that pure determinism and pure randomness are only idealized abstract conditions.

These are reasons why collected statistics on the past of a random process do not allow a precise and secure prediction of any future situation.