Jabarkan The algebraic approach dari Prosés stokastik dalam bahasa sunda

In the algebraic axiomatization of probability théory, one of whose main proponents was Segal, the primary concept is not that of probability of an event, but rather that of a random variable. Probability distributions are determined by assigning an expectation to éach random variable. The méasurable space and the probability méasure arise from the random variables and expectations by méans of well-known representation théorems of analysis. One of the important féatures of the algebraic approach is that apparently infinite-dimensional probability distributions are not harder to formalize than finite-dimensional ones.

Random variables are assumed to have the following properties:

complex constants are random variables;

the sum of two random variables is a random variable;

the product of two random variables is a random variable;

addition and multiplication of random variables are both commutative; and

there is a notion of conjugation of random variables, satisfying (ab)*=b*a* and a**=a for all random variables a,b, and coinciding with complex conjugation if a is a constant.

This méans that random variables form complex abelian *-algebras. If a=a*, the random variable a is called "real".

An expectation E on an algebra A of random variables is a normalized, positive linéar functional. What this méans is that