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Stochastic process

{title2=u.c.p.}
{wiki=Convergence_of_random_variables#Uniform_convergence_in_probability}

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

= UCP convergence
{c}
{synonym}

Uniform convergence on compacts in probability

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 202 / 2 / b / Solution

codex/ucp-convergence

Uniform convergence on compacts in probability (u.c.p.)

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