 Uniform convergence on compacts in probability (source code)

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= Uniform convergence on compacts in probability
{title2=u.c.p.}

= Locally uniform convergence in probability
{synonym}

= UCP convergence
{c}
{synonym}

= Uniformly on compacts in probability
{synonym}

Processes $X_n$ converge uniformly on compacts in probability to $X$ when, for every $T<\infty$ and $\varepsilon>0$,
$$
\mathbb P\!\left(\sup_{t\leq T}|X_n(t)-X(t)|>\varepsilon\right)\to0.
$$

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