# Definition

**Stochastic Process**

A stochastic process is defined to be a function that maps the set to random variable .

**State Space**

Let and be the values of the random variables and B be its

Borel field.State space is denoted by

**σ-Algebra/σ-Field**

Let be the -field of some set , it then must follow

E.g. then an example of the sigma-algebra generated from is .

**Borel Field**

Borel Field or Borel-sigma-algebra generated from is defined as the sigma-algebra of all open subsets of .

### Probability Space

defines a probability space

### Probability Measure

Probability measure

Pis a function which associates a numberP(A)to each set with the following properties:

- Associative properties on disjoint sets , that is

**Note: **See as the probability that the events occurs.

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## 5 thoughts on “Stochastic Process”