Bounded increments
= Bounded increments
{title2=$|X_{n+1}-X_n|\leq C\quad(n\geq0)$}
A discrete-time <stochastic process> has <bounded increments> if a single deterministic $C<\infty$ satisfies $|X_{n+1}-X_n|\leq C$ almost surely for every $n$. The constant is uniform in time and sample outcome; bounding each increment by a different constant does not suffice. This property applies to differences, so it does not require the process itself to stay bounded.