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In this paper, we consider the Dirichlet problem associated to an elliptic Kirchhoff-type equation depending on two parameters. Under rather general and natural assumptions, we prove that, for certain values of the parameters, the problem…
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…
The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…
A profile likelihood ratio test is proposed for inferences on the index coefficients in generalized single-index models. Key features include its simplicity in implementation, invariance against parametrization, and exhibiting substantially…
We introduce a Bayesian solution for the problem in forensic speaker recognition, where there may be very little background material for estimating score calibration parameters. We work within the Bayesian paradigm of evidence reporting and…
In this paper, two generalized algorithms for solving the variational inequality problem in Banach spaces are proposed. Then the strong convergence of the sequences generated by these algorithms will be proved under the suitable conditions.…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
The classical D'Alembert's Ratio Test is a powerful test that we learn from calculus to determine convergence for a series of positive terms. Its range of applicability and ease of computation makes this test extremely appealing. However,…
We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.
We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to…
There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…
We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem two approaches based on the approximation of the objective function by consensus-based particle optimization methods on…
Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data…
By using the strong approximation, this paper establishes several limit results on the convergent rate of a infinite series of probabilities on the other law of iterated logarithm.
A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology…
Motivated by questions in cryptography, we look for diophantine equations that are hard to solve but for which determining the number of solutions is easy.
We consider the exterior free boundary Bernoulli problem in the case of a rough given domain. An asymptotic analysis shows that the solution of the initial problem can be approximated by the solution of a non-rough Bernoulli problem at…
In order to adapt the Wasserstein distance to the large sample multivariate non-parametric two-sample problem, making its application computationally feasible, permutation tests based on the Sinkhorn divergence between probability vectors…
Let $p_n$ denote the probability that a random instance of the stable roommates problem of size $n$ admits a solution. We derive an explicit formula for $p_n$ and compute exact values of $p_n$ for $n\leq 12$.