Geodesic
On the Kolmogorov--Hajek--R\'enyi inequality for normed integrals of weakly dependent processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 2, pp. 225-238

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We consider a process of the form $\zeta_\varepsilon(t)=\sqrt{\varepsilon}\int_0^{t/\varepsilon}\eta(s)\,ds$, $t\in [0,1]$, where $\eta(t)$, $t\ge0$, is a strictly stationary process with zero mean satisfying either the uniform strong mixing condition or the absolute regularity condition and find an estimate from below for the probability of the event that $|\zeta_{\varepsilon}(t)|$, $t\in [0,1]$, lies within a domain with growing curved boundaries.
Keywords: uniformly strong mixing, absolute regularity, spiral, representation.
Mots-clés : martingale 
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     author = {B. V. Bondarev},
     title = {On the {Kolmogorov--Hajek--R\'enyi} inequality for normed integrals of weakly dependent processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {225--238},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_2_a0/}
}
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B. V. Bondarev. On the Kolmogorov--Hajek--R\'enyi inequality for normed integrals of weakly dependent processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 2, pp. 225-238. http://geodesic.mathdoc.fr/item/TVP_1997_42_2_a0/