Locating the maximum of a simple random sequence by sequential search

Consider a stationary Gaussian process with EX_{i}X_{j}=a^{|i-j|} where 0 nd let 0 . It is shown that to locate the maximum of X_{l}, X_{2}, \cdots, X_{N} for large N with probability r , roughly -rN \log a/\log\log N observations at sequentially determined locations are both sufficient and necessary.