A note on LDP for supremum of Gaussian processes over infinite horizon

✍ Scribed by Krzysztof Dȩbicki

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 98 KB
• Volume: 44
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(99)00011-5

✦ Synopsis

The aim of this paper is to give a short proof of a large deviation result for supremum of nencentered Gaussian process over inÿnite horizon. We study family { X; d; u ; u ¿ 0} of Borel probability measures on R, where

for Borel B ⊂ R, drift function d(t) and centered Gaussian processes {X (t); t¿0} with variance function 2 (t). We assume that for each 0 ¡ 61

We obtain logarithmic asymptotic of P(sup t¿0 (X (t) -d(t)) ¿ u). Under additional assumption, that 2 (t) is regularly varying at ∞ and d(t) is linear, we prove large deviation principle for { X; d; u ; u ¿ 0}.