= Absorption time
{title2=$T_A=\inf\{m\geq0:X_m\in A\}$}
For a discrete-time <Markov chain> and a set $A$ of <absorbing states>, its absorption time is the <hitting time> $T_A=\inf\{m\geq0:X_m\in A\}$. It is zero when the initial state already lies in $A$, and infinite on a <sample path> that never enters $A$. Finiteness <almost surely> need not imply a finite <expected value>. For a finite-state model, a uniform positive <probability> of absorption within a fixed number of steps gives a <geometric series> bound on the survival <probabilities> and proves that the <mean> is finite. The <mean absorption time of a lazy symmetric random walk> is an explicit example.
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