It means that, under certain conditions, the empirical frequencies of all events in a certain event-family converge to their theoretical probabilities. Definitions · Proof of uniform convergence...

These random variables converge in distribution to a uniform U(0, 1), whereas their densities do not converge at all. Convergence of measures · Proofs · Fatou's lemma · Borel–Cantelli lemma

10 окт. 2019 г. · That is, limn→∞P(supy∈Y|Xyn−Xy|>ε)=0∀ε>0. This appears to be the standard definition of uniform convergence in probability. However, it seems to ... Uniform convergence in probability Uniform Convergence of random variable on a compact set Uniform convergence implies convergence in expectation ... Convergence of series of uniform random variables Другие результаты с сайта math.stackexchange.com

5 нояб. 2015 г. · Since we already know uniform convergence =⇒ pointwise convergence this proof is omitted, but we include a proof that shows pointwise ...

For example, if Yn is uniform on {1,...,n} and Xn = Yn/n, then Xn converges in distribution to a random variable which is uniform on [0, 1] (exercise).

An equivalent definition of uniform convergence is as follows: Theorem 11.1 gn(x) converges uniformly to g(x) if and only if supx |gn(x) − g(x)| → 0.

6 июн. 2024 г. · The aim of this paper is to review and clarify some facts concern- ing the uniform convergence of statistics like ¯ Xn and random variables ...

In this paper, a set of sufficient conditions for this is given, and we show how these results may be applied to some statistical problems.

12 мая 2009 г. · n σ(θ). We consider convergence in distribution or in probability, uniform with respect to a family of probability distribu- tions.

The notion of convergence in distribution, uniform with respect to the family of probability distributions is not new, but it is usually only marginally.