Related papers: On the boundedness of Bernoulli processes
We show an invariance result for the L2-torsion of groups under uniform measure equivalence provided a measure-theoretic version of the determinant conjecture holds. The measure-theoretic determinant conjecture is discussed and, for…
We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves…
We study the exterior and interior Bernoulli problems for the half Laplacian and the interior Bernoulli problem for the spectral half Laplacian. We concentrate on the existence and geometric properties of solutions. Our main results are the…
We consider the standard thermodynamic processes with constraints, but with additional uncertainty about the control parameters. Motivated by inductive reasoning, we assign prior distribution that provides a rational guess about likely…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
We study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks…
Scale invariant scattering suggests that all Bernoulli numbers B_{2n} can be naturally partitioned, i.e., written as particular finite sums of same-signed, monotonic, rational numbers. Some properties of these rational numbers are discussed…
The Bernoulli filter is a Bayes filter for joint detection and tracking of a target in the presence of false and miss detections. This paper presents a mathematical formulation of the Bernoulli filter in the framework of possibility theory,…
Consider a finite renewal process in the sense that interrenewal times are positive i.i.d. variables and the total number of renewals is a random variable, independent of interrenewal times. A finite point process can be obtained by…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
We give a derivation of tagged particle processes from unlabeled interacting Brownian motions. We give a criteria of the non-explosion property of tagged particle processes. We prove the quasi-regularity of Dirichlet forms describing the…
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
This elementary treatment first summarizes extreme values of a Bernoulli random walk on the one-dimensional integer lattice over a finite discrete time interval. Both the symmetric (unbiased) and asymmetric (biased) cases are discussed.…
We present a randomization-based inferential framework for experiments characterized by a strongly ignorable assignment mechanism where units have independent probabilities of receiving treatment. Previous works on randomization tests often…
A novel multinomial theorem for commutative idempotents is shown to lead to new results about the moments, central moments, factorial moments, and their generating functions for any random variable $X = \sum_{i} Y_i $ expressible as a sum…
We develop a new multi-scale framework flexible enough to solve a number of problems involving embedding random sequences into random sequences. Grimmett, Liggett and Richthammer asked whether there exists an increasing M-Lipschitz…
The generalized labeled multi-Bernoulli (GLMB) is a family of tractable models that alleviates the limitations of the Poisson family in dynamic Bayesian inference of point processes. In this paper, we derive closed form expressions for the…
Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence…
In this paper we prove a strong law of large numbers and its L^1-convergence counterpart for the process counted with a random characteristic in the context of self-similar fragmentation processes. This result extends a somewhat analogical…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…