Related papers: A Note on Uniform Integrability of Random Variable…

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…

Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of…

Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…

A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform…

In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…

WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the…

We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…

We investigate the convergence of series of random variables with second exponential moments. We give sufficient conditions for the convergence of these series with respect to an exponential Orlicz norm and almost surely. Applying this…

Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…

As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…

We investigate the complete $p$-th moment convergence for weighted sums of independent, identically distributed random variables under sublinear expectations space. Using moment inequality and truncation methods, we prove the equivalent…

The main purpose of this paper is to establish a noncommutative analogue of the Efron--Stein inequality, which bounds the variance of a general function of some independent random variables. Moreover, we state an operator version including…

In the framework of variable exponent Sobolev spaces, we prove that the variational eigenvalues defined by inf sup procedures of Rayleigh ratios for the Luxemburg norms are all stable under uniform convergence of the exponents.

We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…

In this paper we investigate algorithmic randomness on more general spaces than the Cantor space, namely computable metric spaces. To do this, we first develop a unified framework allowing computations with probability measures. We show…

Based on existing ideas in the field of imprecise probabilities, we present a new approach for assessing the reliability of the individual predictions of a generative probabilistic classifier. We call this approach robustness…

We give sharp, uniform estimates for the probability that the empirical distribution function for n uniform-[0,1] random variables stays to one side of a given line.

In statistical physics lately a specific kind of average, called the q-expectation value, has been extensively used in the context of q-generalized statistics dealing with distributions following power-laws. In this context q-expectation…

We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random…

In this paper, we present a new classifier, which integrates significance testing results over different random subspaces to yield consensus p-values for quantifying the uncertainty of classification decision. The null hypothesis is that…