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Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…

Optimization and Control · Mathematics 2022-07-05 Christian Kanzow , Patrick Mehlitz

We study the estimation of the invariant density of additive fractional stochastic differential equations with Hurst parameter $H \in (0,1)$. We first focus on continuous observations and develop a kernel-based estimator achieving faster…

Statistics Theory · Mathematics 2025-12-23 Chiara Amorino , Eulalia Nualart , Fabien Panloup , Julian Sieber

We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener…

Numerical Analysis · Mathematics 2022-03-02 Zhihui Liu , Zhonghua Qiao

We consider a class of stochastic control problems with a delayed control, both in drift and diffusion, of the type dX t = $\alpha$ t--d (bdt + $\sigma$dW t). We provide a new characterization of the solution in terms of a set of Riccati…

Optimization and Control · Mathematics 2021-02-25 William Lefebvre , Enzo Miller

Solving large tensor linear systems poses significant challenges due to the high volume of data stored, and it only becomes more challenging when some of the data is missing. Recently, Ma et al. showed that this problem can be tackled using…

Numerical Analysis · Mathematics 2026-05-28 Anna Ma , Deanna Needell , Alexander Xue

In this paper, we propose a monotone approximation scheme for a class of fully nonlinear degenerate partial integro-differential equations (PIDEs) which characterize the nonlinear $\alpha$-stable L\'{e}vy processes under sublinear…

Probability · Mathematics 2024-06-12 Mingshang Hu , Lianzi Jiang , Gechun Liang

We present a form of stratified MCMC algorithm built with non-reversible stochastic dynamics in mind. It can also be viewed as a generalization of the exact milestoning method, or form of NEUS. We prove convergence of the method under…

Probability · Mathematics 2022-02-21 Gabriel Earle , Jonathan Mattingly

This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…

Probability · Mathematics 2014-02-11 Kai Liu

We consider stochastic differential equations in a Hilbert space, perturbed by the gradient of a convex potential. We investigate the problem of convergence of a sequence of such processes. We propose applications of this method to…

Probability · Mathematics 2007-05-23 Lorenzo Zambotti

This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic…

Numerical Analysis · Mathematics 2015-06-18 B. Leimkuhler , C. Matthews , M. V. Tretyakov

Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two different types of irregularities:…

Numerical Analysis · Mathematics 2024-01-12 Kathrin Spendier , Michaela Szölgyenyi

We study the numerical approximation of a class of degenerate parabolic stochastic partial differential equations on non-compact metric graphs, which naturally arise in the asymptotic analysis of Hamiltonian flows under small noise…

Numerical Analysis · Mathematics 2026-04-14 Jianbo Cui , Mihály Kovács , Derui Sheng

We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…

Computation · Statistics 2016-04-26 Gavin A. Whitaker , Andrew Golightly , Richard J. Boys , Chris Sherlock

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of…

Probability · Mathematics 2009-01-20 Istvan Gyöngy , Annie Millet

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…

Optimization and Control · Mathematics 2021-01-14 Caroline Geiersbach , Teresa Scarinci

We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…

Probability · Mathematics 2017-03-24 Hanchao Wang , Zhengyan Lin , Zhonggen Su

In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We…

Numerical Analysis · Mathematics 2025-07-21 Naiyu Jiang , Wendi Bao , Lili Xing , Weiguo Li

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…

Probability · Mathematics 2014-06-17 Erfan Salavati , Bijan Z. Zangeneh

Motivated by weak convergence results in the paper of Takahashi and Yoshida (2005), we show strong convergence for an accelerated Euler-Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the…

Computational Finance · Quantitative Finance 2013-12-02 Hideyuki Tanaka , Toshihiro Yamada

In this paper, we consider Caputo type fractional stochastic time-delay system with permutable matrices. We derive stochastic analogue of variation of constants formula via a newly defined delayed Mittag-Leffer type matrix function. Thus,…

Dynamical Systems · Mathematics 2020-09-23 Arzu Ahmadova , Ismail T. Huseynov , Nazim I. Mahmudov