**A. Rackauskas, C. Suquet**

## Hölder versions of Banach space valued random fields

**abstract:**

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.