New posts in probability-limit-theorems

Asymptotics of $\max\limits_{1\leqslant k\leqslant n}X_k/n$

Rate of convergence in the central limit theorem (Lindeberg–Lévy)

Two questions about uniform integrability

Almost certain non-existence of limit

$ \lim_{n \to \infty} \mathbb{E} \big[ -\frac{1}{n}\ln (1+e^{-nf(X_n)}) \big] = 0 $ [closed]

What is the probability that the sum of digits of a random $k$-digit number is $n$?

Convergence of series $\sum\limits_{k=1}^\infty\frac{1}{X_1+\dots+X_k}$ with $(X_k)$ i.i.d. non integrable

How often was the most frequent coupon chosen?

Given an ergodic property that guarantees convergence of sample means to an expectation, how can I bound the Cesàro Mean of expectation of terms?

Showing uniform integrability to prove the limit of expectation

$ \frac{(1+o_p(1) )A_n}{(1+o(1) )E[A_n]}=\frac{A_n}{E[A_n]}+ o_p(\frac{A_n}{E[A_n]}) ??$

Probability and measure theory

Weak Law of Large Numbers for Dependent Random Variables with Bounded Covariance