= Constant-drift hitting-time identity
{title2=$\mathbb E_xT=f(x)/\delta$}
For a finite <Markov chain>, let $T$ be the first <hitting time> of $D$, assume $T<\infty$ <almost surely>, $f=0$ on $D$ and $Pf=f-\delta$ on its complement, with $\delta>0$. The <stopped martingale> $f(X_{n\wedge T})+\delta(n\wedge T)$ has mean $f(x)$. Boundedness of $f$ and <bounded convergence theorem> give $\mathbb E f(X_{n\wedge T})\to0$; <monotone convergence> then gives the stated finite <expected hitting time>. No drift condition is required after entry into $D$.
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