PROBABILITY TAILS OF GAUSSIAN EXTREMA

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:38

Article

关键词: GAUSSIAN PROCESSES;    ISONORMAL PROCESS;    SUPREMUM;    METRIC ENTROPY;    BROWNIAN SHEET;    EMPIRICAL PROCESSES;   

DOI  :  10.1016/0304-4149(91)90072-K

来源: Elsevier

【 摘 要 】

We study the supremum of 'the' standard isonormal linear process L on a subset C of a real Hilbert space H. Upper and lower bounds on the probability that sup(x-epsilon-C) Lx > lambda, lambda large, are found. We treat a number of examples. These include the distribution of the maximum of certain 'locally stationary' processes on R1, as well as those of the rectangle indexed, pinned Brownian sheet in R(k) and the half-plane indexed pinned sheet in R2. We also consider Brownian motion indexed by convex sets in [0, 1]2.

【 授权许可】

Free