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We establish (i) stability of Lyapunov exponents and (ii) convergence in probability of Oseledets spaces for semi-invertible matrix cocycles, subjected to small random perturbations. The first part extends results of Ledrappier and Young to…

Dynamical Systems · Mathematics 2013-10-10 Gary Froyland , Cecilia González-Tokman , Anthony Quas

We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…

Optimization and Control · Mathematics 2022-01-12 Tobias Breiten , Carsten Hartmann , Lara Neureither , Upanshu Sharma

A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not…

Statistical Mechanics · Physics 2024-05-20 Benjamin Ertel , Udo Seifert

Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…

Dynamical Systems · Mathematics 2025-02-04 David Sabin-Miller , Daniel M. Abrams

We investigate nonequilibrium steady-state dynamics in both continuous- and discrete-state stochastic processes. Our analysis focuses on planar diffusion dynamics and their coarse-grained approximations by discrete-state Markov chains.…

Statistical Mechanics · Physics 2026-05-12 Ramón Nartallo-Kaluarachchi , Renaud Lambiotte , Alain Goriely

Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…

Probability · Mathematics 2011-06-28 Marc Arnaudon , Clément Dombry , Anthony Phan , Le Yang

This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing…

Machine Learning · Computer Science 2025-11-07 Hans Harder , Abhijeet Vishwasrao , Luca Guastoni , Ricardo Vinuesa , Sebastian Peitz

Entropy production (EP) is a central measure in nonequilibrium thermodynamics, as it can quantify the irreversibility of a process as well as its energy dissipation in special cases. Using the time-reversal asymmetry in a system's path…

Statistical Mechanics · Physics 2022-04-26 Dong-Kyum Kim , Sangyun Lee , Hawoong Jeong

We present a new framework for analysing the Expectation Maximization (EM) algorithm. Drawing on recent advances in the theory of gradient flows over Euclidean-Wasserstein spaces, we extend techniques from alternating minimization in…

Machine Learning · Statistics 2025-11-21 Rocco Caprio , Adam M Johansen

An algorithm is proposed for computing equilibrium averages of Markov chains which suffer from metastability -- the tendency to remain in one or more subsets of state space for long time intervals. The algorithm, called the parallel replica…

Numerical Analysis · Mathematics 2015-11-06 David Aristoff

Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…

Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…

Statistical Mechanics · Physics 2024-01-18 Juan De Gregorio , David Sanchez , Raul Toral

This paper describes a method to estimate a production frontier that satisfies the axioms of monotonicity and concavity in a non-parametric Bayesian setting. An inefficiency term that allows for significant departure from prior…

Methodology · Statistics 2015-10-08 José Luis Preciado Arreola , Andrew L. Johnson

As sample sizes grow, scalability has become a central concern in the development of Markov chain Monte Carlo (MCMC) methods. One general approach to this problem, exemplified by the popular stochastic gradient Langevin dynamics (SGLD)…

Computation · Statistics 2024-12-04 Natesh S. Pillai , Aaron Smith , Azeem Zaman

This paper aims to provide some tools coming from functional inequalities to deal with quasi-stationarity for absorbed Markov processes. First, it is shown how a Poincar\'e inequality related to a suitable Doob transform entails exponential…

Probability · Mathematics 2021-03-29 William Oçafrain

We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles2015) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin…

Numerical Analysis · Mathematics 2019-08-13 Michael B. Giles , Mateusz B. Majka , Lukasz Szpruch , Sebastian Vollmer , Konstantinos Zygalakis

We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…

Fluid Dynamics · Physics 2014-11-25 Keith Myerscough , Jason Frank , Benedict Leimkuhler

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

The optimization problems defining meta-stable or stationary equilibrium are explored. The Gibbs scheme is modified aiming to describe the statistical properties of a class of non-equilibrium and metastable states. The system is assumed to…

Statistical Mechanics · Physics 2007-09-04 Alejandro Cabo , Sergio Curilef

We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The…

Statistical Mechanics · Physics 2016-03-23 Rüdiger Kürsten , Ulrich Behn