All Questions

I am interested under what conditions Cramer's theorem applies in random variables taking values in Hilbert spaces. Following these lecture notes, but using a Hilbert space: Let $X_1,X_2,\cdots$, be ...

Let $(X_1,X_2,\cdots)$ be a sequence of independent and identically distributed random variables taking values in some general normed space $(V,||\cdot||)$. Denote $\mu=E[X_1]$ and $S_n=\frac{1}{n}[...

Let two (countably-generated) $\sigma-$algebras $\mathscr{F,G}$ on the event space $\mathbb{R}$ be given. I believe we also need the atoms of $\mathscr{F,G}$ to be the points of $\mathbb{R}$. Let $\...

$H$ is (Shannon) entropy. In terms of the positive real number $t$, what distribution(s) $\hspace{.01 in}X$ on $\:[0\hspace{.005 in},\hspace{-0.03 in}\scriptsize+\normalsize\infty\hspace{-0.02 in})$...

Let $\mathcal{P}(\mathbb{R}^d)$ the space of probability measures on $\mathbb{R}^d$ with total variation metric $\delta$, fix $k \in \mathbb{N}$, and let $\mathcal{P}'\subset \mathcal{P}(\mathbb{R}^d)$...