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Let $(X_{n,k})_{k=1,\ldots,n}^{n\in\mathbb{N}}$ be a triangular array of random variables with finite moments of all orders, with no assumptions on their independence. Suppose that $$ \mathbb{E}\left[ …

If $m,n \to \infty$ with $\frac{m}n \to \lambda \in (0,\infty)$ (let's suppose that $n$ depends on $m \in\mathbb{N}$), and if you are saying that each $\mathbf{B} = \mathbf{B}_m$ is an $m\times n$ ran …

In probability theory, the term subexponential distribution has historically been used for a distribution whose CDF $F(x)$ satisfies the relation $$ n(1-F(x)) \sim 1 - F^{*n}(x) $$ for any $n \ge 1$ a …

For convenience, let's say that I have a locally compact Hausdorff space $X$ and am concerned with probability measures on its Borel $\sigma$-algebra $\mathcal{B}(X)$. Natural vector spaces to conside …