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We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation we…

Data Analysis, Statistics and Probability · Physics 2010-07-02 Andreas Ruttor , Manfred Opper

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…

Quantitative Methods · Quantitative Biology 2017-01-13 David Schnoerr , Guido Sanguinetti , Ramon Grima

The simplest, and most common, stochastic model for population processes, including those from biochemistry and cell biology, are continuous time Markov chains. Simulation of such models is often relatively straightforward as there are…

Probability · Mathematics 2012-03-01 David F. Anderson , Masanori Koyama

A general class of stochastic gene expression models with self regulation is considered. One or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The gene or genes are self regulating…

Molecular Networks · Quantitative Biology 2014-12-30 Jay Newby

We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times…

Physics and Society · Physics 2007-05-23 Marian Anghel , Kenneth A. Werley , Adilson E. Motter

This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for…

Probability · Mathematics 2014-01-03 Jose Blanchet , Peter Glynn , Shuheng Zheng

The paper deals with a problem of control of a system characterized by the fact that the influence of controls on the dynamics of certain functions of state variables (called observables) is relatively weak and the rates of change of these…

Optimization and Control · Mathematics 2016-08-12 Vladimir Gaitsgory , Sergey Rossomakhine

We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…

Machine Learning · Statistics 2023-10-25 Felix X. -F. Ye , Sichen Yang , Mauro Maggioni

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

We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…

Machine Learning · Computer Science 2024-08-28 Yuan Chen , Dongbin Xiu

The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found…

Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such…

Molecular Networks · Quantitative Biology 2025-11-03 Juan David Marmolejo Lozano , Nikola Popovic , Ramon Grima

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

In this paper, we consider a class of nonautonomous multi-scale stochastic partial differential equations with fully local monotone coefficients. By introducing the evolution system of measures for time-inhomogeneous Markov semigroups, we…

Probability · Mathematics 2025-09-03 Mengyu Cheng , Xiaobin Sun , Yingchao Xie

The application of the quasi-steady-state approximation to the Michaelis-Menten reaction embedded in large open chemical reaction networks is a popular model reduction technique in deterministic and stochastic simulations of biochemical…

Statistical Mechanics · Physics 2013-05-28 Philipp Thomas , Arthur V. Straube , Ramon Grima

Multi-Agent Reinforcement Learning involves agents that learn together in a shared environment, leading to emergent dynamics sensitive to initial conditions and parameter variations. A Dynamical Systems approach, which studies the evolution…

Multiagent Systems · Computer Science 2025-01-03 David Goll , Jobst Heitzig , Wolfram Barfuss

We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…

Statistical Finance · Quantitative Finance 2015-09-30 Yuriy Stepanov , Philip Rinn , Thomas Guhr , Joachim Peinke , Rudi Schäfer

Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…

Methodology · Statistics 2025-01-08 Siliang Zhang , Yunxiao Chen

A perturbation framework is developed to analyze metastable behavior in stochastic processes with random internal and external states. The process is assumed to be under weak noise conditions, and the case where the deterministic limit is…

Analysis of PDEs · Mathematics 2013-09-23 Jay Newby , Jon Chapman

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

Dynamical Systems · Mathematics 2015-01-22 Carmeline J. Dsilva , Ronen Talmon , C. William Gear , Ronald R. Coifman , Ioannis G. Kevrekidis