Strong law for submartingales with bounded increments
= Strong law for submartingales with bounded increments
{title2=$\liminf_nY_n/n\geq0\text{ a.s.}$}
If a <submartingale> has uniformly <bounded increments>, then $\liminf_n Y_n/n\geq0$ almost surely. In its <Doob decomposition in discrete time>, the predictable compensator is nondecreasing, while the martingale part has <bounded increments>. The <strong law for martingales with bounded increments> makes the latter negligible on the linear scale.