Related papers: Moment bounds for IID sequences under sublinear ex…
We show that the delay time distribution for wave reflection from a one-dimensional random potential is related directly to that of the reflection coefficient, derived with an arbitrarily small but uniform imaginary part added to the random…
Estimating frequency moments of data streams is a very well studied problem and tight bounds are known on the amount of space that is necessary and sufficient when the stream is adversarially ordered. Recently, motivated by various…
In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. Using information-theoretic methods, we derive a lower…
In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of…
Suppose a sequence of random variables {X_n} has negative drift when above a certain threshold and has increments bounded in L^p. When p>2 this implies that EX_n is bounded above by a constant independent of n and the particular sequence…
Peng, S. (\cite{P08b}) proved the law of large numbers under a sublinear expectation. In this paper, we give its error estimates by Stein's method.
We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive systems. These conditions generalize, extend, and strengthen many existing results. Different types of input-to-state stability (ISS), as well as…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…
In this paper, we address the problem of bounding conditional expectations when moment information of the underlying distribution and the random event conditioned upon are given. To this end, we propose an adapted version of the generalized…
We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…
Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors,…
We consider a system of $N$ Hawkes processes and observe the actions of a subpopulation of size $K \le N$ up to time $t$, where $K$ is large. The influence relationships between each pair of individuals are modeled by i.i.d.Bernoulli($p$)…
We prove by counterexample that a large deviation principle established by Chen and Feng [{\em Comm. Statist. Theory Methods} {\bf 45} (2016), 400--412] in the framework of sublinear expectations is incorrect. That implies that the rate…
We present new estimators for the statistical analysis of the dependence of the mean gap time length between consecutive recurrent events, on a set of explanatory random variables and in the presence of right censoring. The dependence is…
We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…
Consider a sequence of $n$ independent random variables with a common continuous distribution $F$, and consider the task of choosing an increasing subsequence where the observations are revealed sequentially and where an observation must be…