  For the moving average process $X_n=\rho \xi_{n-1}+\xi_n$, $n\in\mathbb{N}$,
where $\rho\in\mathbb{R}$ and $(\xi_i)_{i\ge -1}$ is an i.i.d. sequence of
normally distributed random variables, we study the persistence probabilities
$\mathbb{P}(X_0\ge 0,\dots, X_N\ge 0)$, for $N\to\infty$. We exploit that the
exponential decay rate $\lambda_\rho$ of that quantity, called the persistence
exponent, is given by the leading eigenvalue of a concrete integral operator.
This makes it possible to study the problem with purely functional analytic
methods. In particular, using methods from perturbation theory, we show that
the persistence exponent $\lambda_\rho$ can be expressed as a power series in
$\rho$. Finally, we consider the persistence problem for the Slepian process,
transform it into the moving average setup, and show that our perturbation
results are applicable.
