Differentiating sigma-fields for Gaussian and shifted Gaussian processes

Sébastien Darses (1) , Ivan Nourdin (1) , Giovanni Peccati (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LSTA - Laboratoire de Statistique Théorique et Appliquée

We study the notions of differentiating and non-differentiating sigma-fields in the general framework of (possibly drifted) Gaussian processes, and characterize their invariance properties under equivalent changes of probability measure. As an application, we investigate the class of stochastic derivatives associated with shifted fractional Brownian motions. We finally establish conditions for the existence of a jointly measurable version of the differentiated process, and we outline a general framework for stochastic embedded equations.

Domaines: Probabilités [math.PR]

Sébastien Darses, Ivan Nourdin, Giovanni Peccati. Differentiating sigma-fields for Gaussian and shifted Gaussian processes. 2007. ⟨hal-00128162⟩