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In this paper we construct a framework for doing statistical inference for discretely observed stochastic differential equations (SDEs) where the driving noise has 'memory'. Classical SDE models for inference assume the driving noise to be…

Methodology · Statistics 2013-07-05 Martin Lysy , Natesh S. Pillai

Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of…

Probability · Mathematics 2016-04-26 Daniel Gerth , Andreas Hofinger , Ronny Ramlau

The computer algebra routines documented here empower you to reproduce and check many of the details described by an article on large deviations for slow-fast stochastic systems [abs:1001.4826]. We consider a 'small' spatial domain with two…

Dynamical Systems · Mathematics 2012-04-23 A. J. Roberts

This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following…

Physics and Society · Physics 2025-12-04 Raphael Korbmacher , Parthib Khound , Antoine Tordeux , Frank Gronwald

Mean field approximation is a powerful technique which has been used in many settings to study large-scale stochastic systems. In the case of two-timescale systems, the approximation is obtained by a combination of scaling arguments and the…

Probability · Mathematics 2023-01-24 Sebastian Allmeier , Nicolas Gast

We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space-time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the…

Probability · Mathematics 2015-10-05 Tusheng Zhang

We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We…

Adaptation and Self-Organizing Systems · Physics 2020-08-26 Igor Franović , Serhiy Yanchuk , Sebastian Eydam , Iva Bačić , Matthias Wolfrum

Polyhomeostatic adaption occurs when evolving systems try to achieve a target distribution function for certain dynamical parameters, a generalization of the notion of homeostasis. Here we consider a single rate encoding leaky integrator…

Adaptation and Self-Organizing Systems · Physics 2013-07-15 Mathias Linkerhand , Claudius Gros

A continuous-time average consensus system is a linear dynamical system defined over a graph, where each node has its own state value that evolves according to a simultaneous linear differential equation. A node is allowed to interact with…

Optimization and Control · Mathematics 2023-03-31 Tadashi Wadayama , Ayano Nakai-Kasai

This article proposes for stochastic partial differential equations (SPDEs) driven by additive noise, a novel approach for the approximate parameterizations of the ``small'' scales by the ``large'' ones, along with the derivaton of the…

Analysis of PDEs · Mathematics 2013-11-14 Mickaël D. Chekroun , Honghu Liu , Shouhong Wang

In this paper, we consider a class of slow-fast systems of stochastic partial differential equations where the nonlinearity in the slow equation is not continuous and unbounded. We first provide conditions that ensure the existence of a…

Probability · Mathematics 2023-01-02 Sandra Cerrai , Yichun Zhu

In this paper, we propose a filtering algorithm for simultaneously estimating the mode, input and state of hidden mode switched linear stochastic systems with unknown inputs. Using a multiple-model approach with a bank of linear input and…

Optimization and Control · Mathematics 2016-06-28 Sze Zheng Yong , Minghui Zhu , Emilio Frazzoli

Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems…

adap-org · Physics 2009-10-30 G. D. Lythe , M. R. E. Proctor

This paper is devoted to studying the averaging principle for fast-slow system of rough differential equations driven by mixed fractional Brownian rough path. The fast component is driven by Brownian motion, while the slow component is…

Probability · Mathematics 2023-03-15 Bin Pei , Yuzuru Inahama , Yong Xu

Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…

Statistical Mechanics · Physics 2017-10-05 Tobias Grafke , Eric Vanden-Eijnden

The issue of white-noise-aided control is considered and its availability is proved. And a noise-aiding way is developed to stabilize perturbed systems to be input-to-state stable (ISS) with respect to (w.r.t.) perturbations. To illustrate…

Optimization and Control · Mathematics 2008-06-24 Wuhua Hu

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…

Probability · Mathematics 2010-11-15 Jian Ren , Hongbo Fu , Daomin Cao , Jinqiao Duan

In this paper, the optimal control for discrete-time systems driven by fractional noises is studied. A stochastic maximum principle is obtained by introducing a backward stochastic difference equation contains both fractional noises and the…

Optimization and Control · Mathematics 2024-12-24 Yuecai Han , Yuhang Li

In this paper we correct an error made in a previous work, where a misleading stochastic system was obtained due to a lapse concerning a sign in one of the equations at the beginning of the work such that the results obtained are quite…

Dynamical Systems · Mathematics 2017-10-03 Tomás Caraballo , María J. Garrido-Atienza , Javier López-de-la-Cruz , Alain Rapaport

The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…

Mathematical Physics · Physics 2012-12-03 Frank Noé , Feliks Nüske