Extremes of Gaussian processes, on results of Piterbarg and Seleznjev

✍ Scribed by J. Hüsler

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 95 KB
• Volume: 44
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(99)00016-4

✦ Synopsis

For a particular sequence of Gaussian processes we consider the maximum Mn(T ) up to time T and its limiting behaviour as T = T (n) and n converges to ∞. This sequence occurs in the approximation of the path of the continuous Gaussian process by broken lines. This limiting behaviour was analyzed by Piterbarg and Seleznjev assuming certain conditions. We improve their result assuming a weaker long-range dependence condition.