ﻻ يوجد ملخص باللغة العربية
Any (measurable) function $K$ from $mathbb{R}^n$ to $mathbb{R}$ defines an operator $mathbf{K}$ acting on random variables $X$ by $mathbf{K}(X)=K(X_1, ldots, X_n)$, where the $X_j$ are independent copies of $X$. The main result of this paper concerns selectors $H$, continuous functions defined in $mathbb{R}^n$ and such that $H(x_1, x_2, ldots, x_n) in {x_1,x_2, ldots, x_n}$. For each such selector $H$ (except for projections onto a single coordinate) there is a unique point $omega_H$ in the interval $(0,1)$ so that for any random variable $X$ the iterates $mathbf{H}^{(N)}$ acting on $X$ converge in distribution as $N to infty$ to the $omega_H$-quantile of $X$.
In this paper, we prove convergence in distribution of Langevin processes in the overdamped asymptotics. The proof relies on the classical perturbed test function (or corrector) method, which is used both to show tightness in path space, and to ident
We consider the probability distributions of values in the complex plane attained by Fourier sums of the form sum_{j=1}^n a_j exp(-2pi i j nu) /sqrt{n} when the frequency nu is drawn uniformly at random from an interval of length 1. If the coefficien
We study the weak limits of solutions to SDEs [dX_n(t)=a_nbigl(X_n(t)bigr),dt+dW(t),] where the sequence ${a_n}$ converges in some sense to $(c_- 1mkern-4.5mumathrm{l}_{x<0}+c_+ 1mkern-4.5mumathrm{l}_{x>0})/x+gammadelta_0$. Here $delta_0$ is the Dira
The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate the zeros of a function that can be written as an expectation. It is known that under some technical assumptions, a Gaussian convergence can be establish
We address the problem of proving a Central Limit Theorem for the empirical optimal transport cost, $sqrt{n}{mathcal{T}_c(P_n,Q)-mathcal{W}_c(P,Q)}$, in the semi discrete case, i.e when the distribution $P$ is finitely supported. We show that the asy