Short Communications: Estimates of the Distribution of the Maximumof a Random Field
| Autor: | E. I. Ostrovskii |
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| Rok vydání: | 1998 |
| Předmět: | |
| Zdroj: | Theory of Probability & Its Applications. 42:302-310 |
| ISSN: | 1095-7219 0040-585X |
| DOI: | 10.1137/s0040585x97976167 |
| Popis: | Let $ \xi(t) $ be a random field with values in $ \bR^1$, defined for $ t \in T,\ T$ an arbitrary set. In this paper two-sided exponential estimates are derived for probabilities $ P(T,u) = \bP\{\sup_{t \in T} \xi(t)\break > u \} $: $$ C_1 g_2(u) \l \log P(T,\,u) + g_1(u) \l C_2 g_2(u), $$ where $ g_1(u) $ is a convex function, $u \to \infty \Rightarrow \lim g_1'(u) = \infty$, $\lim [g_2(u)/g_1(u)] = 0$, $C_k$ are positive numbers independent of~u. |
| Databáze: | OpenAIRE |
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