= Solution
<Markov chain Monte Carlo asymptotic variance> for a stationary <Markov chain> and $\psi\in L^2(\pi)$ is
$$
\sigma_K^2(\psi)
=\lim_{n\to\infty}n\operatorname{Var}\left(
\frac1n\sum_{j=1}^n\psi(X_j)\right)
=\operatorname{Var}_\pi(\psi)
+2\sum_{k=1}^{\infty}
\operatorname{Cov}_\pi(\psi(X_0),\psi(X_k)),
$$
whenever the limit and series exist. If a <reversible Markov chain> has positive $L^2_0(\pi)$ <spectral gap> $\gamma$, then the <spectral theorem for normal operators on a separable Hilbert space> gives
$$
\sigma_K^2(\psi)
\leq\left(\frac2\gamma-1\right)
\operatorname{Var}_\pi(\psi).
$$
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