accurate calculation of reliability index is very important for the reliability analysis of structures. in some limit state functions with nonlinear characteristic and several local optimum design points, the computational reliability methods may not appropriately determine the failure probability, and iterative reliability approaches may be converged to local optimum design points. in this pap...

We show that all modes of convergence in Lt (in probability, almost surely, complete) for the standard kernel regression estimate are equivalent. AMS Subject Classification: Primary 62605.

For a certain class of martingales, the convergence to mixture normal distribution is established under the convergence in distribution for the conditional variance. This is less restrictive in comparison with the classical martingale limit theorem where one generally requires the convergence in probability. The extension removes a main barrier in the applications of the classical martingale li...

In this note we provide a simpler proof of a probabilistic analysis of the set cover problem given in [6]. We also prove these results using the language of high probability instead of using convergence in probability or convergence almost everywhere, making the previous results more precise.

We study Davis-type theorems on the optimal rate of convergence of moderate deviation probabilities. In the case of martingale difference sequences, under the finite pth moments hypothesis (1 ≤ p <∞), and depending on the normalization factor, our results show that Davis’ theorems either hold if and only if p > 2 or fail for all p ≥ 1. This is in sharp contrast with the classical case of i.i.d....

It is shown by example that learning rules of the fictitious play type fail to converge in certain kinds of coordination games. Variants of fictitious play in which past actions are eventually forgotten and that incorporate small stochastic perturbations are better behaved for this class of games: over the long run, players coordinate with probability one. Journal of Economic Literature Classif...

Why are product prices in online markets dispersed in spite of very small search costs? To address this question, we construct a unique dataset from a Japanese price comparison site, which records price quotes offered by e-retailers as well as customers' clicks on products, which occur when they proceed to purchase the product. The novelty of our approach is that we seek to extract useful infor...

The quantum normal form approach to quantum transition state theory is used to compute the cumulative reaction probability for collinear exchange reactions. It is shown that for heavy-atom systems such as the nitrogen-exchange reaction, the quantum normal form approach gives excellent results and has major computational benefits over full reactive scattering approaches. For light atom systems s...

We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...

In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal stationary points. However, existing results on stochastic non-convex optimization are limited, especially with a high probability second-order convergence. W...