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We present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant…

Numerical Analysis · Mathematics 2022-05-10 Xingyuan Chen , Goncalo dos Reis

When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by…

Dynamical Systems · Mathematics 2015-10-13 Miles Crosskey , Mauro Maggioni

We introduce an explicit, adaptive time-stepping scheme for the simulation of SPDEs with one-sided Lipschitz drift coefficients. Strong convergence rates are proven for the full space-time discretisation with multiplicative trace-class…

Numerical Analysis · Mathematics 2019-08-27 Stuart Campbell , Gabriel Lord

On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient. On the other…

Numerical Analysis · Mathematics 2012-09-13 Martin Hutzenthaler , Arnulf Jentzen , Peter E. Kloeden

This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler…

Numerical Analysis · Mathematics 2024-03-28 Chenxu Pang , Xiaojie Wang , Yue Wu

Bayesian inference tasks continue to pose a computational challenge. This especially holds for spatial-temporal modeling where high-dimensional latent parameter spaces are ubiquitous. The methodology of integrated nested Laplace…

Computation · Statistics 2023-03-28 Lisa Gaedke-Merzhäuser , Elias Krainski , Radim Janalik , Håvard Rue , Olaf Schenk

The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…

Numerical Analysis · Mathematics 2025-02-21 Edward M. Terrell , Boyce E. Griffith

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

Machine Learning · Computer Science 2025-06-06 Ruoxi Jiang , Xiao Zhang , Karan Jakhar , Peter Y. Lu , Pedram Hassanzadeh , Michael Maire , Rebecca Willett

We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by additive noise, under a one-sided Lipschitz continuity…

Numerical Analysis · Mathematics 2020-10-02 Charles-Edouard Bréhier

The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…

Statistics Theory · Mathematics 2020-08-28 Mohamed Ndaoud

This paper presents a new formulation for model-free robust optimal regulation of continuous-time nonlinear systems. The proposed reinforcement learning based approach, referred to as incremental adaptive dynamic programming (IADP),…

Systems and Control · Electrical Eng. & Systems 2022-03-25 Cong Li , Yongchao Wang , Fangzhou Liu , Qingchen Liu , Martin Buss

We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which…

Numerical Analysis · Mathematics 2025-09-19 Matteo Croci , Abdul-Lateef Haji-Ali , Ian C. J. Powell

Modeling irregularly-sampled time series (ISTS) is challenging because of missing values. Most existing methods focus on handling ISTS by converting irregularly sampled data into regularly sampled data via imputation. These models assume an…

Artificial Intelligence · Computer Science 2024-08-21 Rohit Agarwal , Aman Sinha , Ayan Vishwakarma , Xavier Coubez , Marianne Clausel , Mathieu Constant , Alexander Horsch , Dilip K. Prasad

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…

Probability · Mathematics 2018-02-20 Vincent Lemaire

In traditional work on numerical schemes for solving stochastic differential equations (SDEs), it is usually assumed that the coefficients are globally Lipschitz. This assumption has been used to establish a powerful analysis of the…

Probability · Mathematics 2017-09-15 Philip Protter , Lisha Qiu , Jaime San Martin

The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of…

Numerical Analysis · Mathematics 2018-08-14 Lukas Einkemmer

This paper concerns the study of the generalized Bolza problem governed by differential inclusions satisfying the so-called "relaxed one-sided Lipschitzian" (ROSL) condition with respect to the state variables subject to various types of…

Optimization and Control · Mathematics 2015-06-02 B. S. Mordukhovich , Yuan Tian

We present a methodology to construct efficient high-order in time accurate numerical schemes for a class of gradient flows with appropriate Lipschitz continuous nonlinearity. There are several ingredients to the strategy: the exponential…

Numerical Analysis · Mathematics 2021-02-23 Wenbin Chen , Shufen Wang , Xiaoming Wang

We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for…

Econometrics · Economics 2022-11-29 Eric Gautier , Christiern Rose

An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…

Numerical Analysis · Mathematics 2024-09-23 Daniel O'Shea , Xiaoran Zhang , Shayan Mohammadian , Chongmin Song