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Fair enough. But I still think perhaps there are interesting things one might be able to say about the category of such objects (if one were to form the category of these sequences of R modules, ca …

(1) (Modified from [1]pp.246-247,312-313) First we sample $Z$ from $Unif[0,1)$, since $\mathbb{R}$ is an Archimedes field, for a fixed $n$ we can find such a $k$ that $\frac{k}{2^n}\leq Z< \frac{k+1}{ …

The problem can be solved if the distribution $f(\cdot)$ is in a Levy stable distribution family. In your concrete example, since the $d\dim$ normal distribution $N(\mu,I_d)$ is "additive", the exact …

No. Vector space structure is not enough, we actually need a compatible lattice structure to make things work. To apply the conditional expectation operator $E(\bullet\mid Y)$ onto the Hilbert space c …

For general Hall Algebra, Ian MacDonald's Symmetric Functions and Hall Polynomials http://books.google.com.hk/books/about/Symmetric_Functions_and_Hall_Polynomials.html?id=srv90XiUbZoC For general re …

I do not think the accepted answer is a complete one. To be honest there is no such a pointless theory as far as I know. And I actually have read the book [Kappos] which could be viewed as a continut …

For two $n \times n$ nonnegative definite Hermitian matrices $A$ and $B$ over the real number field $\mathbb R$: Question1:Is there always a nonsingular matrix $P$ over the same field $F$ whic …

You may want to have a look into Hwang's Lemma which is known as a discrete (sufficient) analogy to Stein's Lemma though it is NOT a characterization. Generally speaking you can yield such a character …

The reference pointed out by Vincent are both thesis, I think a more appropriate introductory level material is Brown&Yin. And it is the only modern paper that I touched tangential to beta expansion. …

...It is well known that the celebrated Hille-Yosida theorem, discovered independently by Hille [1] and Yosida [2], gave the first characterization of the infinitesimal generator of a strongly …

It is aimless to extend "statistical independence" beyond category of $\sigma$-subalgebras and probability-preserving morphisms on a fixed probability space $\prod,\mathcal{A}$ as pointed out by the c …

If you are just concerned with logistic kernels, and you are willing to put a mild assumption on the $\beta$-Hölder function $f$ to be estimated, then [Rousseau] assumes mild condition $\boldsymbol{A} …

On pp.13~15 of Fox, L. Parker. Chebyshev polynomials in numerical analysis. No. 519.4 F6. 1968., especially (64)(65), we can see the arguement. As an approach to the minimax solution to the function $ …

You need a global convexity to enjoy the optimal convergence rate, otherwise even local convexity will almost surely(not in probabilistic sense) lead to the worst rate you pointed out. MCMC(Markov Ch …

This is a well known result from diffusion PDE theory. For example [1] studied the semi-linear equation in form of $$u_t - \Delta u + u^\gamma = 0, \quad (t,x) \in (0,T) \times \mathbb{R}^n, \gamma> …