From invariance principles to a class of multifractional fields related to fractional sheets

Céline Lacaux (1, 2, 3) , Renaud Marty (1)

1 IECN - Institut Élie Cartan de Nancy
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 BIGS - Biology, genetics and statistics

In this paper, we study some invariance principles where the limits are Gaussian random fields sharing many properties with multifractional Brownian sheets. In particular, they satisfy the same type of self-similarity and Hölder regularity properties. We also extend the invariance principles mentioned above in a stable setting.

Keywords: Invariance principle; Multifractional anisotropic random fields; Local self-similarity; Sample path properties

Domains: Probability [math.PR]

Céline Lacaux, Renaud Marty. From invariance principles to a class of multifractional fields related to fractional sheets. 2011. ⟨hal-00592188⟩