Coupling inequality for total variation
= Coupling inequality for total variation
For any coupling of two <Markov chains> and its coalescence time $T$,
$$
\lVert\mathcal L(X_t)-\mathcal L(Y_t)\rVert_{\mathrm{TV}}\leq\mathbb P(T>t).
$$
= Coupling inequality for total variation
For any coupling of two <Markov chains> and its coalescence time $T$,
$$
\lVert\mathcal L(X_t)-\mathcal L(Y_t)\rVert_{\mathrm{TV}}\leq\mathbb P(T>t).
$$