Related papers: Practical Boundary Degeneracy and Reverse-Martinga…
The practicality of the stochastic network calculus (SNC) is often questioned on grounds of potential looseness of its performance bounds. In this paper it is uncovered that for bursty arrival processes (specifically Markov-Modulated On-Off…
In this paper, we are concerned with the reliability assessment of redundant multi-channel systems having multiple controllers with overlapping functionality -- where all controllers are required to respond optimally to the non-faulty…
We study the sequential general online regression, known also as the sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We focus on obtaining tight, often matching, lower and upper…
We consider a flocking system confined transversally between two infinite reflecting parallel walls separated by a distance $L_\perp$. Infinite or periodic boundary conditions are assumed longitudinally to the direction of collective…
Recurrent Neural Networks (RNNs) have achieved great success in the prediction of sequential data. However, their theoretical studies are still lagging behind because of their complex interconnected structures. In this paper, we establish a…
A new formulation of Stochastic Model Predictive Output Feedback Control is presented and analyzed as a translation of Stochastic Optimal Output Feedback Control into a receding horizon setting. This requires lifting the design into a…
We consider the Last-Success-Problem with $n$ independent Bernoulli random variables with parameters $p_i>0$. We improve the lower bound provided by F.T. Bruss for the probability of winning and provide an alternative proof to the one given…
Given a probability measure on a finitely generated group, its Martin boundary is a natural way to compactify the group using the Green function of the corresponding random walk. For finitely supported measures in hyperbolic groups, it is…
As is well known the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit. We identified one reason for this long ago: insufficient decay of the probability density either near infinity or near poles of…
We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. The END structure, as a new benchmark for negative dependence, is comparable to comonotonicity and…
R\'emy's algorithm is a Markov chain that iteratively generates a sequence of random trees in such a way that the $n^{\mathrm{th}}$ tree is uniformly distributed over the set of rooted, planar, binary trees with $2n+1$ vertices. We obtain a…
The bounded mean betting procedure serves as a crucial interface between the domains of (1) sequential, anytime-valid statistical inference, and (2) online learning and portfolio selection algorithms. While recent work in both domains has…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic at every sample size, while controlling the probability of…
We consider the Minimum Description Length principle for online sequence prediction. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is…
Consider estimating the G-formula for the counterfactual mean outcome under a given treatment regime in a longitudinal study. Bang and Robins provided an estimator for this quantity that relies on a sequential regression formulation of this…
Regularized linear regression is central to machine learning, yet its high-dimensional behavior with informative priors remains poorly understood. We provide the first exact asymptotic characterization of training and test risks for maximum…
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…
This paper studies when a sequence of probability measures on a metric space admit subsequential weak limits. A sufficient condition called sequential tightness is formulated, which relaxes some assumptions for asymptotic tightness used in…