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13 papers · 1 filter
The rate of convergence of the Walk on Spheres Algorithm
Ilia Binder, Mark Braverman
In this paper we examine the rate of convergence of one of the standard algorithms for emulating exit probabilities of Brownian motion, the Walk on Spheres (WoS) algorithm. We obta…
Discrete time nonlinear filters with informative observations are stable
Ramon van Handel
The nonlinear filter associated with the discrete time signal-observation model is known to forget its initial condition as regardless of the observation s…
Bayesian sequential change diagnosis
Savas Dayanik, Christian Goulding, H. Vincent Poor
Sequential change diagnosis is the joint problem of detection and identification of a sudden and unobservable change in the distribution of a random sequence. In this problem, the…
Regression estimation from an individual stable sequence
Gusztav Morvai, Sanjeev R. Kulkarni, Andrew B. Nobel
We consider univariate regression estimation from an individual (non-random) sequence , which is stable in the sense that for each…
The two possible values of the chromatic number of a random graph
Dimitris Achlioptas, Assaf Naor
Given d \in (0,infty) let k_d be the smallest integer k such that d < 2k\log k. We prove that the chromatic number of a random graph G(n,d/n) is either k_d or k_d+1 almost surely.
A Berry-Esseen type inequality for convex bodies with an unconditional basis
Bo'az Klartag
We provide a sharp rate of convergence in the central limit theorem for random vectors with an unconditional, log-concave density. The argument relies on analysis of the Neumann la…