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Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…

Machine Learning · Computer Science 2025-06-11 Linus Heck , Maximilian Gelbrecht , Michael T. Schaub , Niklas Boers

Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…

Methodology · Statistics 2021-02-01 Théo Michelot , Richard Glennie , Catriona Harris , Len Thomas

Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although…

Machine Learning · Computer Science 2026-05-18 Yuantu Zhu , Zheyan Li , Dai Shi , Luke Thompson , Oliver Nash , Jose Miguel Lara Rangel , Siran Li , Bingguang Chen , Rongchan Zhu , Qi Meng , Hao Ni

We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…

Statistics Theory · Mathematics 2025-03-31 Shohei Nakajima

System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…

Computational Physics · Physics 2020-10-14 Constantino A. Garcia , Paulo Felix , Jesus M. Presedo , Abraham Otero

A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…

Data Analysis, Statistics and Probability · Physics 2016-11-25 Daniel Peavoy , Christian L. E. Franzke , Gareth O. Roberts

We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the…

Methodology · Statistics 2025-09-17 Yujie Zhao , Xiaoming Huo , Yajun Mei

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…

Optimization and Control · Mathematics 2026-05-19 Begoña García Malaxechebarría , Courtney Paquette , Maryam Fazel , Dmitriy Drusvyatskiy

We prove a general criterion providing sufficient conditions under which a time-discretiziation of a given Stochastic Differential Equation (SDE) is a uniform in time approximation of the SDE. The criterion is also, to a certain extent,…

Numerical Analysis · Mathematics 2025-01-22 Letizia Angeli , Dan Crisan , Michela Ottobre

We investigate existence, uniqueness and approximation of solutions to stochastic delay differential equations (SDDEs) under Carath\'eodory-type drift coefficients. Moreover, we also assume that both drift $f=f(t,x,z)$ and diffusion…

Numerical Analysis · Mathematics 2023-06-16 Paweł Przybyłowicz , Yue Wu , Xinheng Xie

In a previous work by the first author with J. Turi (AMO, 08), a stochastic variational inequality has been introduced to model an elasto-plastic oscillator with noise. A major advantage of the stochastic variational inequality is to…

Numerical Analysis · Mathematics 2011-12-21 Alain Bensoussan , Hector Jasso Fuentes , Laurent Mertz

In this paper, we investigate numerically the stochastic ABC model, a toy model in the theory of astrophysical kinematic dynamos, within the recently proposed supersymmetric theory of stochastics (STS). STS characterises stochastic…

Chaotic Dynamics · Physics 2018-06-19 Igor V. Ovchinnikov , Yuquan Sun , Torsten A. Ensslin , Kang. L. Wang

We study the ergodic properties of a class of controlled stochastic differential equations (SDEs) driven by $\alpha$-stable processes which arise as the limiting equations of multiclass queueing models in the Halfin-Whitt regime that have…

Probability · Mathematics 2019-07-22 Ari Arapostathis , Hassan Hmedi , Guodong Pang , Nikola Sandrić

To support mechanism online learning and facilitate digital twin development for biomanufacturing processes, this paper develops an efficient Bayesian inference approach for partially observed enzymatic stochastic reaction network (SRN), a…

Machine Learning · Statistics 2024-07-02 Wandi Xu , Wei Xie

Metropolized integrators for ergodic stochastic differential equations (SDE) are proposed which (i) are ergodic with respect to the (known) equilibrium distribution of the SDE and (ii) approximate pathwise the solutions of the SDE on finite…

Numerical Analysis · Mathematics 2010-01-13 Nawaf Bou-Rabee , Eric Vanden-Eijnden

We propose a tractable semiparametric estimation method for structural dynamic discrete choice models. The distribution of additive utility shocks in the proposed framework is modeled by location-scale mixtures of extreme value…

Econometrics · Economics 2023-08-15 Andriy Norets , Kenichi Shimizu

In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…

Statistics Theory · Mathematics 2017-10-16 Trisha Maitra , Sourabh Bhattacharya

In order to inherit numerically the ergodicity of the damped stochastic nonlinear Schr\"odinger equation with additive noise, we propose a fully discrete scheme, whose spatial direction is based on spectral Galerkin method and temporal…

Numerical Analysis · Mathematics 2016-06-07 Chuchu Chen , Jialin Hong , Xu Wang

In this paper we study an Ergodic Markovian BSDE involving a forward process $X$ that solves an infinite dimensional forward stochastic evolution equation with multiplicative and possibly degenerate diffusion coefficient. A concavity…

Optimization and Control · Mathematics 2019-10-14 G. Guatteri , G. Tessitore

This paper deals with the process $X = (X_t)_{t\in [0,T]}$ defined by the stochastic differential equation (SDE) $dX_t = (a(X_t) + b(Y_t))dt +\sigma(X_t)dW_1(t)$, where $W_1$ is a Brownian motion and $Y$ is an exogenous process. The first…

Statistics Theory · Mathematics 2025-07-09 Fabienne Comte , Nicolas Marie