# 20th European Young Statisticians Meeting

14-18 August 2017
Uppsala University
Europe/Stockholm timezone

## Estimates for distributions of Hölder semi-norms of random processes from spaces F_ψ(Ω)

16 Aug 2017, 14:30
30m
Ångströmslaboratoriet (Uppsala University)

Speaker

### 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)

### Presentation Materials

 Paper
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