Cooling down stochastic differential equations: Almost sure convergence [PDF]
Stochastic Processes and their Applications, 2022 We consider almost sure convergence of the SDE $dX_t=α_t d t + β_t d W_t$ under the existence of a $C^2$-Lyapunov function $F:\mathbb R^d \to \mathbb R$. More explicitly, we show that on the event that the process stays local we have almost sure convergence in the Lyapunov function $(F(X_t))$ as well as $\nabla F(X_t)\to 0$, if $|β_t|=\mathcal O( t^{-β}
Steffen Dereich, Sebastian Kassing
semanticscholar +5 more sources
Almost-sure convergence of iterates and multipliers in stochastic sequential quadratic optimization [PDF]
Journal of Optimization Theory and Applications, 2023 Stochastic sequential quadratic optimization (SQP) methods for solving continuous optimization problems with nonlinear equality constraints have attracted attention recently, such as for solving large-scale data-fitting problems subject to nonconvex ...
Frank E. Curtis, Xin Jiang, Qi Wang
openalex +3 more sources
Almost Sure Convergence for the Maximum and Minimum of Normal Vector Sequences [PDF]
Mathematics, 2020 In this paper, we prove the almost sure convergences for the maximum and minimum of nonstationary and stationary standardized normal vector sequences under some suitable conditions.
Zhicheng Chen +2 more
doaj +2 more sources
Almost sure convergence on chaoses [PDF]
Proceedings of the American Mathematical Society, 2018 We present several new phenomena about almost sure convergence on homogeneous chaoses that include Gaussian Wiener chaos and homogeneous sums in independent random variables.
Guillaume Poly, Guangqu Zheng
semanticscholar +5 more sources
Almost sure convergence of randomised‐difference descent algorithm for stochastic convex optimisation [PDF]
IET Control Theory & Applications, 2021 Stochastic gradient descent algorithm is a classical and useful method for stochastic optimisation. While stochastic gradient descent has been theoretically investigated for decades and successfully applied in machine learning such as training of deep ...
Xiaoxue Geng, Gao Huang, Wenxiao Zhao
doaj +2 more sources
Almost Sure Convergence for Angelesco Ensembles [PDF]
, 2011 25 pages.sections 6 and 7 added with proof of large ...
Thomas Bloom
openalex +3 more sources
Almost Sure Convergence of Liouville First Passage Percolation [PDF]
Probability Theory and Related Fields, 2023 Liouville first passage percolation (LFPP) with parameter $ξ> 0$ is the family of random distance functions (metrics) $(D_h^ε)_{ε> 0}$ on $\mathbb{C}$ obtained heuristically by integrating $e^{ξh}$ along paths, where $h$ is a variant of the Gaussian free field.
Charles Devlin VI
openalex +3 more sources
Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator [PDF]
, 2015 The aim of this paper is to introduce the concept of generalized ϕ-weakly contraction random operators and then to prove the convergence and almost sure T-stability of Mann and Ishikawa-type random iterative schemes.
Godwin Amechi Okeke, Mujahid Abbas
openalex +2 more sources
Lp and almost sure rates of convergence of averaged stochastic gradient algorithms: locally strongly convex objective [PDF]
E S A I M: Probability & Statistics, 2016 An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are efficient ...
Antoine Godichon‐Baggioni
openalex +3 more sources
Convergence and Almost Sure Polynomial Stability of Partially Truncated Split-Step Theta Method for Stochastic Pantograph Models with Lévy Jumps [PDF]
MathematicsThis paper addresses a stochastic pantograph model with Lévy leaps where non-jump coefficients exceed linearity. The partially truncated split-step theta method is introduced and applied to the proposed model.
Amr Abosenna, Ghada AlNemer, Boping Tian
doaj +2 more sources