Large deviations of infinite intersections of events in Gaussian processes
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- 作者：Michel Mandjes ; Petteri Mannersalo ; Ilkka Norros and Miranda van Uitert
- 关键词：Sample-path large deviations ; Dominating point ; Reproducing kernel Hilbert space ; Minimum norm problem ; Fractional Brownian motion ; Busy period
- 刊名：Stochastic Processes and their Applications
- 出版年：2006
- 出版时间：September 2006
- 年：2006
- 卷：116
- 期：9
- 页码：1269-1293
- 全文大小：572 K
文摘
Consider events of the form WA-A-W-D-MsSAYVA-UUA-U-AAZCWAYZVU-AAZWDEEVVU-VWUDWZZU-D-U&_acct=C000050221&_version=1&_userid=10&md5=f346388e3cf73fde14f1e0bceae36208"" title=""Click to view the MathML source"">{Zs≥ζ(s),sS}, where w the MathML source"">Z is a continuous Gaussian process with stationary increments, w the MathML source"">ζ is a function that belongs to the reproducing kernel Hilbert space w the MathML source"">R of process w the MathML source"">Z, and is compact. The main problem considered in this paper is identifying the function da20"" title=""Click to view the MathML source"">β*R satisfying w the MathML source"">β*(s)≥ζ(s) on w the MathML source"">S and having minimal w the MathML source"">R-norm. The smoothness (mean square differentiability) of w the MathML source"">Z turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when w the MathML source"">ζ(s)=s for w the MathML source"">s[0,1] and w the MathML source"">Z is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process.