Abstract: Letbe a Borel function applied to a stationary, possibly long-memory, sequence of standard Gaussian random variables
. Define the first passage time
, for partial sums
. Suppose
has finite positive mean
. When
itself is positive or its negative part is under some moment conditions, it is proved that
for
as
tends to infinity.
Key words and phrases: Elementary renewal theorem, first passage time, Gaussian sequence, long-memory, long-range dependence, self-similar.