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We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift is the superposition operator associated…

Analysis of PDEs · Mathematics 2018-10-03 Carlo Marinelli , Luca Scarpa

Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…

Machine Learning · Computer Science 2026-05-21 Jianhong Chen , Naichen Shi , Xubo Yue

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of…

Probability · Mathematics 2015-05-19 Kestutis Kubilius , Viktor Skorniakov , Dmitrij Melichov

The notion of concept drift refers to the phenomenon that the data generating distribution changes over time; as a consequence machine learning models may become inaccurate and need adjustment. In this paper we consider the problem of…

Machine Learning · Computer Science 2022-05-16 Fabian Hinder , André Artelt , Valerie Vaquet , Barbara Hammer

We construct a stochastic process whose drift is a function of the process's local time at a reflecting barrier. The process arose as a model of the interactions of a Brownian particle and an inert particle in (Knight, 2001). Interesting…

Probability · Mathematics 2007-05-23 David White

We consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on discrete observations of solution to the stochastic…

Probability · Mathematics 2013-09-26 Yuliya Mishura , Kostiantyn Ral'chenko , Oleg Seleznev , Georgiy Shevchenko

In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…

Probability · Mathematics 2016-10-23 Mark Freidlin , Leonid Koralov

The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence of big data and machine learning methodology. Discovering governing equations and quantifying dynamical properties of…

Dynamical Systems · Mathematics 2021-12-10 Min Dai , Jinqiao Duan , Jianyu Hu , Xiangjun Wang

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

Machine Learning · Computer Science 2020-01-09 Junteng Jia , Austin R. Benson

It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct…

Probability · Mathematics 2010-10-26 Kei Kobayashi

We study a stochastic differential equation with an unbounded drift and general H\"older continuous noise of an arbitrary order. The corresponding equation turns out to have a unique solution that, depending on a particular shape of the…

Probability · Mathematics 2021-12-15 Giulia Di Nunno , Yuliya Mishura , Anton Yurchenko-Tytarenko

We study the effect of stochastic sampling on the estimation of the drift parameter of continuous time AR(1) process. A natural distribution free moment estimator is considered for the drift based on stochastically observed time points. The…

Statistics Theory · Mathematics 2013-07-29 Radhendushka Srivastava , Ping Li

Drift is a significant issue that undermines the reliability of gas sensors. This paper introduces a probabilistic model to distinguish between environmental variation and instrumental drift, using low-cost non-dispersive infrared (NDIR)…

Signal Processing · Electrical Eng. & Systems 2025-02-07 Cheng Yang , Gustav Bohlin , Tobias Oechtering

Wind power is playing an increasingly important role in electricity markets. However, it's inherent variability and uncertainty cause operational challenges and costs as more operating reserves are needed to maintain system reliability.…

Optimization and Control · Mathematics 2016-03-01 Yishen Wang , Zhi Zhou , Cong Liu , Audun Botterud

Generating high quality uncertainty estimates for sequential regression, particularly deep recurrent networks, remains a challenging and open problem. Existing approaches often make restrictive assumptions (such as stationarity) yet still…

Machine Learning · Computer Science 2021-07-26 Jiri Navratil , Matthew Arnold , Benjamin Elder

Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless,…

Methodology · Statistics 2020-04-02 Tomáš Rubín , Victor M. Panaretos

This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…

Machine Learning · Statistics 2026-04-01 Yuzhen Zhao , Yating Liu , Marc Hoffmann

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…

Machine Learning · Computer Science 2025-02-03 Macheng Shen , Chen Cheng

We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean field approach to sandpile dynamics by formulating it as…

Adaptation and Self-Organizing Systems · Physics 2009-11-13 Martin Rypdal , Kristoffer Rypdal

We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating…

Numerical Analysis · Mathematics 2021-06-08 Assyr Abdulle , Giacomo Garegnani , Grigorios A. Pavliotis , Andrew M. Stuart , Andrea Zanoni