A. Rackauskas, C. Suquet

Hölder versions of Banach space valued random fields

For rather general moduli of smoothness $\rho$, like $\rho(h)\!=\!h^\alpha \ln^\beta (c/h)$, we consider the H\"older spaces $\Hr(B)$ of functions $[0,1]^d \to B$ where $B$ is a separable Banach space. We establish an isomorphism between $\Hr(B)$ and some sequence Banach space. With this analytical tool, we follow a very natural way to study, in terms of {\em second differences}, the existence of a version in $\Hr(B)$ for a given random field.