相关论文: Weak Convergence of Probability Measures

The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes…

This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…

Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…

The book is structured into four main chapters. Chapter 1 introduces the foundational concepts of divergence measures, including the well-known Kullback-Leibler divergence and its limitations. It then presents a detailed exploration of…

Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give…

We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when…

We propose a new approach to vague convergence of measures based on the general theory of boundedness due to Hu (1966). The article explains how this connects and unifies several frequently used types of vague convergence from the…

Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…

In this paper, weak convergences of marked empirical processes in $L^2(\mathbb{R},\nu)$ and their applications to statistical goodness-of-fit tests are provided, where $L^2(\mathbb{R},\nu)$ is the set of equivalence classes of the square…

This note proves a weak type of the sharpness principle as conjectured by Gneiting, Balabdaoui, and Raftery in 2007 in connection with probabilistic forecasting subject to calibration constraints. A strong version of such a principle still…

This article employs the relation between probabilities of two consecutive values of a Poisson random variable to derive conditions for the weak convergence of point processes to a Poisson process. As applications, we consider the starting…

The standard textbook method for estimating the probability of a biased coin from finite tosses implicitly assumes the sample sizes are large and gives incorrect results for small samples. We describe the exact solution, which is correct…

This article constructs a class of random probability measures based on exponentially and polynomially tilting operated on the laws of completely random measures. The class is proved to be conjugate in that it covers both prior and…

Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…

This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…

Assuming that $(X_t)_{t\in\Z}$ is a vector valued time series with a common marginal distribution admitting a density $f$, our aim is to provide a wide range of consistent estimators of $f$. We consider different methods of estimation of…

We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…

In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…

We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. Using the idea of weak measurement, we study Hardy's gedanken experiment and show how the "negative…

We review the definition and the concepts of the weak values and some measurement model to extract the weak value. This material is based on the author Ph.D. thesis "Time in Weak Values and Discrete Time Quantum Walk" at Tokyo Institute of…