Discrete Stochastic Processes and Optimal Filtering

1.1. Definitions and general properties

If we remember that , the set of real n -tuples can be fitted to two laws: and making it a vector space of dimension n .

The basis implicitly considered on will be the canonical base = (1, 0,…,0),…, = (0,…,0,1) and x ∈ expressed in this base will be denoted:

Definition of a real random vector

Beginning with a basic definition, without concerning ourselves at the moment with its rigor: we can say simply that a real vector linked to a physical or biological phenomenon is random if the value taken by this vector is unknown and the phenomenon is not completed. ...