Gaussian process

It's a stochastic process (Xt) with t Є R+, where random variables constituting the random vector n-dimensional (Xt1, Xt2, Xt3, …, Xtn) for ∀n Є N, versus time (t1, t2, t3, …, tn) per ∀n Є R+, are distributed as a multivariate Gaussian distribution, according to the following equation for the probability density:

              

Where b represents the expected value of the random variable function versus time and K the covariance between the random variables.

                                     

 

                         

Note that this process is uniquely determined by assigning the functions:

                   

where K is a symmetric function and semi positive definite.

 

Editor: Giuliano DI TOMMASO