Related papers: Running minimum in the best-choice problem
A collaborative distributed binary decision problem is considered. Two statisticians are required to declare the correct probability measure of two jointly distributed memoryless process, denoted by $X^n=(X_1,\dots,X_n)$ and…
The problem of simultaneously testing the marginal distributions of sequentially monitored, independent data streams is considered. The decisions for the various testing problems can be made at different times, using data from all streams,…
Consider the Euclidean traveling salesman problem with $n$ random points on the plane. Suppose that one of the points is shifted to a new random location. This gives us a new optimal path. Consider such shifts for each of the $n$ points. Do…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…
This paper develops a time-inconsistent and path-dependent singular control framework incorporating a running minimum process. We derive a verification theorem that characterizes equilibria under substantially weaker regularity conditions…
We study the asymptotic behavior of the maximum interpoint distance of random points in a $d$-dimensional set with a unique diameter and a smooth boundary at the poles. Instead of investigating only a fixed number of $n$ points as $n$ tends…
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…
Finding outlying elements in probability distributions can be a hard problem. Taking a real example from Voting Rights Act enforcement, we consider the problem of maximizing the number of simultaneous majority-minority districts in a…
We obtain the best possible upper bounds for the moments of a single order statistic from independent, non-negative random variables, in terms of the population mean. The main result covers the independent identically distributed case.…
In this paper, we study the hypothesis testing problem of, among $n$ random variables, determining $k$ random variables which have different probability distributions from the rest $(n-k)$ random variables. Instead of using separate…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
We investigate a model of continuous-time simple random walk paths in $\mathbb{Z}^d$ undergoing two competing interactions: an attractive one towards the large values of a random potential, and a self-repellent one in the spirit of the…
We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the…
Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…
The run-and-tumble walk, consisting in randomly reoriented ballistic excursions, models phenomena ranging from gas kinetics to bacteria motility. We evaluate the mean time required for this walk to find a fixed target within a 2D or 3D…
We consider the Random Euclidean Assignment Problem in dimension $d=1$, with linear cost function. In this version of the problem, in general, there is a large degeneracy of the ground state, i.e. there are many different optimal matchings…
The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the…
We study the problem of bounding path-dependent expectations (within any finite time horizon $d$) over the class of discrete-time martingales whose marginal distributions lie within a prescribed tolerance of a given collection of benchmark…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…