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)
