Tagged Questions

Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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weighted restricted integer compositions and extended binomial coefficients [on hold]

proof of d_{S,f}(n,k) = \binom{k}{n}{(f(s)){s\in S}}
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Random walk on d-dimensional torus

I am reading the following paper: http://arxiv.org/pdf/1602.03849v2.pdf I will explain the general setup below. Let $x\in X=\mathbb{T}^d$, where $\mathbb{T}^d$ is the d dimensional torus. Let $\rho$ ...
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Hierarchical (Recursive) Random Walk Model

Consider the following hierarchical (recursive) random walk model. For the first level $\ell=1$, let $\{X_t^{(\ell)}\}_{t=1}^{T}$ be a (discrete) random walk. For the next level $\ell=2$, we ...
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Random Cantor sets on the unit interval

Denote $A=\{0\}, B=\{0,1\}$. Then any subset of $\Omega:=\{A,B\}^{\mathbb N}$ is a continuum provided the number of $B$'s is infinite. We treat these as binary expansions of numbers in $[0,1]$. For ...
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How to sample a uniform random polyomino?

A polyomino is formed by joining finitely many unit squares edge to edge. It may be regarded as a finite subset of the regular square tiling with a connected interior. In particular, for us, ...
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Reference on Probability theory on functional spaces (in special Hilbert spaces)

Currently, I am working on some sort of stochastic optimization problems defined over function spaces. I am familiar with standard probability theory (R. Durrett, ''Probability: Theory and Examples")...
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Variation on stones in buckets

This is a spinoff, see Collecting stones in n buckets. Frankly speaking my only motivation is that I became curious: what happens if one redistributes the stones into the same buckets? More ...
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Meaningful formalization of a continuum of Bernoulli random variables [closed]

I was wondering if there is a meaningful formalization for a continuum of Bernoulli random variables. Informally speaking, consider the interval $[0,1]$, and let's say that for every $x \in [0,1]$, ...
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Tail bound for product of normal distribution

Let $U, V$ be two standard normal random variables with covariance $cov(U,V) = \beta \in [0,1)$. Let $W = UV$ be the product of two RV's, and $W_1, W_2, \ldots, W_n$ be n i.i.d copies of $W$, what's ...
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Symmetry of concentration bounds on mean

Question summary: If I have a two-sided bound, can I immediately get a one-sided bound with tighter constants? Question details: Let $\mathbf X = X_1,...,X_n$ be $n$ i.i.d. real-valued random ...
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It shall be an old story in PDE. I am looking for a sufficient condition of Dirichlet problem for the existence of the unique viscosity solution of the equation in the form of $$\inf_{a \in [-1,1]} \{... 0answers 134 views Order statistics of iid uniform RV and Pólya's urn model. Question about a.s. convergence Let U_1,U_2,U_3,\dots be IID uniform on [0,1]. For each n\geq 1 let$$U_{1:n}<U_{2:n}<\dots<U_{n:n} be the order statistic of $(U_1,\dots,U_n)$. Independent of the $U$ process there ...
I am studying the asymptotic properties of a dynamic a model involving the difference of two balanced Poisson processes (i.e., $\lambda_1 = \lambda_2$). I recently discovered the Skellam Distribution ...