اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Local Limit Theorem for Robbins-Monro Procedure
65
0
0.0
(
0
)
تأليف
Lorick Huang
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 established for the procedure. Here, we are interested in the local limit theorem, that is, quantifying this convergence on the density of the involved objects. The analysis relies on a parametrix technique for Markov chains converging to diffusions, where the drift is unbounded.
قيم البحث
اقرأ أيضاً
We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by a Gaussian random velocity field that is white in time and smooth in space. We show that conditional on the velocity field, the quenched density of the p
article after a long time can be approximated pointwise by the product of a deterministic Gaussian density and a spacetime-stationary random field $U$. If the velocity field is additionally assumed to be incompressible, then $Uequiv 1$ almost surely and we obtain a local central limit theorem.
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 $X$.
As proved by Regnier and Rosler, the number of key comparisons required by the randomized sorting algorithm QuickSort to sort a list of $n$ distinct items (keys) satisfies a global distributional limit theorem. Fill and Janson proved results about th
e limiting distribution and the rate of convergence, and used these to prove a result part way towards a corresponding local limit theorem. In this paper we use a multi-round smoothing technique to prove the full local limit theorem.
We define a multi-group version of the mean-field spin model, also called Curie-Weiss model. It is known that, in the high temperature regime of this model, a central limit theorem holds for the vector of suitably scaled group magnetisations, that is
the sum of spins belonging to each group. In this article, we prove a local central limit theorem for the group magnetisations in the high temperature regime.
We propose a boundary regularity condition for the $M_n(mathbb{C})$-valued subordination functions in free probability to prove the local limit theorem and delocalization of eigenvectors for polynomials in two random matrices. We prove this through e
stimating the pair of $M_n(mathbb{C})$-valued approximate subordination functions for the sum of two $M_n(mathbb{C})$-valued random matrices $gamma_1otimes C_N+gamma_2otimes U_N^*D_NU_N$, where $C_N$, $D_N$ are deterministic diagonal matrices, and $U_N$ is Haar unitary.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
