Derivatives of a stochastic process via Jacobian/Hessian of covariance: stationary case

Antonio Sala, UPV

Difficulty: ***** ,       Relevance: ,      Duration: 13:54

*Enlace a Spanish version

Summary:

This video applies the formulae in video [gradgpEN], about the derivatives of a stochastic process, to a stationary case. In that case, covariance $k(x,x^{\prime })$ only depends on the difference between the points $k(x,x^{\prime })=\kappa (x^{\prime }-x)$. Actually, the results are a direct application of the formulae in the referred video but, given that the stationary case is very frequent in applications, it is worth explicitly obtaining the expressions for such a popular use case.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.