= Strong law for martingales with bounded increments
{title2=$M_n/n\to0\text{ a.s.}$}
= Bounded-increment martingale strong law
{synonym}
If a <martingale> has increments bounded by a single deterministic constant, then $M_n/n\to0$ almost surely. Its increments form a uniformly $L^2$-bounded <martingale difference sequence>; apply the <strong law for uniformly L2-bounded uncorrelated random variables> to their partial sums and note $M_0/n\to0$. No square-integrability of the initial value is needed beyond the usual martingale integrability.
Back to article page
