Kolmogorov-Bochner theorem

It is the theorem according to which if the distribution Ft defined in R, known in an interval T consists of t Є T (t1, t2, t3, ..., tn) for ∀ n Є R, it is verified that {Ft}tЄT is compatible, then there exists a unique probability function:

                         

                                              

It follows that the finite-dimensional distributions determine uniquely the distribution of the whole process.

 

Editor: Giuliano DI TOMMASO