New posts in Probability Limit Theorems

Using Central Limit Theorem to approximate.

If $X_n$ converges in distribution to $X$, is it true that $\alpha_n X_n$ converges to $ \alpha X$ as well?

Probability and measure theory

Limit value of the product martingale $\exp(uX_n - nu^2 \sigma^2 / 2)$

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

Applying Central Limit Theorem to show that $E\left(\frac{|S_n|}{\sqrt{n}}\right) \to \sqrt{\frac{2}{\pi}}\sigma$