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The stochastic thermodynamics of a dilute, well-stirred mixture of chemically-reacting species is built on the stochastic trajectories of reaction events obtained from the Chemical Master Equation. However, when the molecular populations…

Statistical Mechanics · Physics 2017-07-04 Jordan M. Horowitz

Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…

Probability · Mathematics 2025-07-15 David F. Anderson , Aidan S. Howells

Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…

Mathematical Physics · Physics 2023-05-31 Chris D Greenman

A microscopic heterogeneous system under random influence is considered. The randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium. This system is modeled by a…

Analysis of PDEs · Mathematics 2009-11-13 Wei Wang , Jinqiao Duan

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…

Chaotic Dynamics · Physics 2024-05-14 Ludovico Theo Giorgini , Andre N. Souza , Peter J. Schmid

Traditional stochastic modeling of reactive systems limits the domain of applicability of the associated path thermodynamics to systems involving a single elementary reaction at the origin of each observed change in composition. An…

Statistical Mechanics · Physics 2023-01-18 F. Baras , A. L. Garcia , M. Malek Mansour

The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is…

Chemical Physics · Physics 2015-06-18 Maria Bruna , S. Jonathan Chapman , Matthew J. Smith

We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…

Computation · Statistics 2016-04-26 Gavin A. Whitaker , Andrew Golightly , Richard J. Boys , Chris Sherlock

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…

Optimization and Control · Mathematics 2019-05-28 Lukáš Adam , Martin Branda

A stochastic system under the influence of a stochastic environment is correlated with both present and future states of the environment. Such a system can be seen as implicitly implementing a predictive model of future environmental…

Statistical Mechanics · Physics 2018-10-05 Matthew E. Quenneville , David A. Sivak

High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…

Fluid Dynamics · Physics 2024-11-20 Javier Jiménez

In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists' ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate…

Quantitative Methods · Quantitative Biology 2022-07-27 Zhou Fang , Ankit Gupta , Mustafa Khammash

Understanding the physics of non-equilibrium systems remains as one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the…

Soft Condensed Matter · Physics 2016-11-17 A. Lasanta , Pablo I. Hurtado , A. Prados

Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…

Analysis of PDEs · Mathematics 2026-02-23 Marzia Bisi , Davide Cusseddu , Ana Jacinta Soares , Romina Travaglini

We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within…

Statistical Mechanics · Physics 2015-12-18 L. Bertini , A. De Sole , D. Gabrielli , G. Jona-Lasinio , C. Landim

In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…

Probability · Mathematics 2018-10-18 Hakima Bessaih , Yalchin Efendiev , Razvan Florian Maris

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

We address the problem of estimating steady-state quantities associated to systems of stochastic chemical kinetics. In most cases of interest these systems are analytically intractable, and one has to resort to computational methods to…

Quantitative Methods · Quantitative Biology 2014-01-21 Andreas Milias-Argeitis , John Lygeros , Mustafa Khammash

A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called…

Biological Physics · Physics 2010-05-18 Pavel M. Lushnikov , Nan Chen , Mark Alber

We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…

Mathematical Physics · Physics 2009-08-18 Enrique Hernandez-Lemus , Jesus K. Estrada-Gil