相关论文: Weak Convergence of Probability Measures

In this paper we introduce a notion of tightness for a family of nonlinear expectations and show that the tightness can be applied to obtain weak compactness in a framework of nonlinear expectation space. This criterion is very useful for…

The main aim of this article is to give an exposition of weak convergence, Prohorov theorem and Prohorov spaces. In this context we study the relationship between Levy distance $\ell(F, G)$ between two distribution functions $F$ and $G$ and…

We consider an extension of $\epsilon$-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the…

We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze…

A weak measurement consists in coupling a system to a probe in such a way that constructive interference generates a large output. So far, only the average output of the probe and its variance were studied. Here, the characteristic function…

The measures of roughness of the volatility in the litterature are based on the realized volatility of high frequency data. Some authors show that this leads to a biased estimate, and does not necessarily indicate roughness of the…

Weak values are average quantities,therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as…

In the literature, quite a few measures have been proposed for quantifying the deviation of a probability distribution from symmetry. The most popular of these skewness measures are based on the third centralized moment and on quantiles.…

We derive tight and computable bounds on the bias of statistical estimators, or more generally of quantities of interest, when evaluated on a baseline model P rather than on the typically unknown true model Q. Our proposed method combines…

It is well known that the Poisson-Boltzmann (PB) equation yields the exact counterion density around charged objects in the weak coupling limit. In this paper we generalize the PB approach to account for coupling of arbitrary strength by…

Convergence rate estimates in limit theorems for sums of independent random variables are considered.

The exact conditions on valid pointer states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any pointer state with vanishing probability current density. This condition is found both for…

I review aspects of the theory of the weak interaction in a set of lectures originally presented at the 2016 CERN-JINR European School of Particle Physics. The topics discussed are: (1) the experimental basis of the V-A structure of the…

Several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. Recently, a new generalization of…

The weak lensing surveys have the potential to probe directly the clustering statistics of dark matter in the universe. Recent studies have shown that it is possible to predict analytically the whole probability distribution function (pdf)…

There is suggested a version of the experiment with a correlated pair of particles in the entangled state. The experiment demonstrates that, in the case of weak and/or non-demolition measurements of one of the particles, it is possible to…

Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…

The association between a continuous and an ordinal variable is commonly modeled through the polyserial correlation model. However, this model, which is based on a partially-latent normality assumption, may be misspecified in practice, due…

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

The main purpose of this short article is to give a brief overview of the development of the very interesting weak measurement protocol. I add some comments relating to the reality of weak values, and also comment on the allowed values of…