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 < a < 1,
nd let
0 < r < 1
. 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.