### Speaker

Mr
Dmytro Zatula
(Taras Shevchenko National University of Kyiv)

### Description

In the following we deal with estimates for distributions of Hölder semi-norms of sample functions of random processes from spaces $\mathbb{F}_\psi(\Omega)$, defined on a compact metric space and on an infinite interval $[0,\infty)$, i.e. probabilities
$$\mathsf{P}\left\{\sup\limits_{\substack{0<\rho(t,s)\le\varepsilon \\ t,s\in\mathbb{T}}} \frac{|X(t)-X(s)|}{f(\rho(t,s))}>x\right\}.$$
Such estimates and assumptions under which semi-norms of sample functions of random processes from spaces $\mathbb{F}_\psi(\Omega)$, defined on a compact space, satisfy the Hölder condition were obtained by Kozachenko and Zatula (2015). Similar results were provided for Gaussian processes, defined on a compact space, by Dudley (1973). Kozachenko (1985) generalized Dudley's results for random processes belonging to Orlicz spaces, see also Buldygin and Kozachenko (2000). Marcus and Rosen (2008) obtained $L^p$ moduli of continuity for a wide class of continuous Gaussian processes. Kozachenko et al. (2011) studied the Lipschitz continuity of generalized sub-Gaussian processes and provided estimates for the distribution of Lipschitz norms of such processes. But all these problems were not considered yet for processes, defined on an infinite interval.

### Primary author

Mr
Dmytro Zatula
(Taras Shevchenko National University of Kyiv)