Results 81 to 90 of about 4,276 (212)

Convergence Theorems for Partial Sums of Arbitrary Stochastic Sequences

Journal of Inequalities and Applications, 2010
By using Doob's martingale convergence theorem, this paper presents a class of strong limit theorems for arbitrary stochastic sequence. Chow's two strong limit theorems for martingale-difference sequence and Loève's and Petrov's strong limit ...
Wang Xiaosheng, Guo Haiying
doaj  

Fixed accuracy confidence intervals for variance under first-order stationary autoregressive processes

Research in Statistics
A sequential procedure is developed to construct a fixed accuracy confidence interval (CI) of the common unknown variance of the random observations, where the observations arise from a first-order stationary autoregressive (AR(1)) process with a ...
Rahul Bhattacharya, Uttam Bandyopadhyay, Atanu Biswas, Pritam Sarkar   +3 more
doaj   +1 more source

Frequency‐dependent contraction rates for the Bayesian method to the inverse source problem

Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.
Abstract This paper addresses an inverse source problem for acoustic waves in a range of frequencies. Our study has two main goals. First, although the problem is severely ill‐posed with a logarithmic stability estimate, we demonstrate, through careful analysis of the forward map's singular values, that increasing the frequency range enhances stability,
Pu‐Zhao Kow, Jenn‐Nan Wang
wiley   +1 more source

Stochastic Gradient Descent in High Dimensions for Multi‐Spiked Tensor PCA

Communications on Pure and Applied Mathematics, Volume 79, Issue 10, Page 2291-2369, October 2026.
ABSTRACT We study the high‐dimensional dynamics of online stochastic gradient descent (SGD) for the multi‐spiked tensor model. This multi‐index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the goal is to estimate the unknown signal vectors within the N$N$‐dimensional unit sphere through maximum ...
Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo   +2 more
wiley   +1 more source

Long-Time Behavior of Galton–Watson Systems with Circular Mechanism

Mathematics
Let {Zn:n≥0} be a Galton–Watson system with a circular mechanism a∗b, where a={aj}j=0∞ and b={bj}j=0∞ are probability distributions on Z+:={0,1,2,⋯}. Let ma:=∑j=0∞jaj, mb:=∑j=0∞jbj. The extinction property of such branching systems is first studied. Then,
Junping Li, Mixuan Hou
doaj   +1 more source

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

The martingale index: A measure of self-deception in betting and finance

Judgment and Decision Making
People who repeatedly risk money, whether they be traders for financial institutions, corporate executives, day traders, or sports bettors, sometimes appear to do better than chance only because the risk of large losses is hidden or overlooked.
Valentin Dimitrov, Glenn Shafer
doaj   +1 more source

Pricing Equity-Indexed Annuities under Stochastic Interest Rates Using Copulas

Journal of Probability and Statistics, 2010
We develop a consistent evaluation approach for equity-linked insurance products under stochastic interest rates. This pricing approach requires that the premium information of standard insurance products is given exogenously. In order to evaluate equity-
Patrice Gaillardetz
doaj   +1 more source

Robust Tests of Forecast Accuracy for Factor‐Augmented Regressions With an Application to the Novel EA‐MD‐QD Dataset

Journal of Applied Econometrics, Volume 41, Issue 5, Page 549-566, August 2026.
ABSTRACT We present four novel tests of equal predictive accuracy and encompassing á Pitarakis (2023, 2025) for factor‐augmented regressions. Factors are estimated using cross‐section averages (CAs) of grouped series and our theoretical findings are empirically relevant: asymptotic normality, robustness to an overspecification of the number of factors,
Alessandro Morico, Ovidijus Stauskas
wiley   +1 more source

Martingale sinh bởi bước đi ngẫu nhiên một chiều có điều kiện

Tạp chí Khoa học Đại học Cần Thơ
Trong bài báo này, mô hình bước đi ngẫu nhiên một chiều và bước đi ngẫu nhiên một chiều có điều kiện đã được xem xét. Trong khi bước đi ngẫu nhiên là một quá trình martingale thì bước đi ngẫu nhiên có điều kiện lại là một submartingale chặt.
Lê Hoài Nhân, Lâm Hoàng Chương, Dương Thị Bé Ba   +2 more
doaj   +1 more source