Questions tagged [convergence-distribution]

I am working on a problem involving almost sure convergence and Rayleigh distributed random variables, and I need some help to confirm my understanding and approach. The problem is as follows: Let $X_1, X_2, X_3, \ldots$ be a sequence of random…

Let $X_{1},\ldots,X_{N}$ be i.i.d. random variables with mean 0 and variance 1. Assume that $X_{i}$ are continuous random variables with all finite moments and a nice density function. Let \begin{equation} S_{N} =…

I would like to understand how this Theorem implies the subsequent Corollary: Theorem. Let A be an irreducible matrix, related to a continuous time Markov branching process $X(t)$, with dominant eigenvalue $\lambda_1$ and associated eigenvector…

The issue is that I have to prove the following with limited resources. Problem: Let $X_n$ and $Y_n$ be p-dimensional random vectors. Show that if $X_n − Y_n \xrightarrow{P} 0$ and $X_n \xrightarrow{D} X$ , where $X$ is a p-dimensional random…