Nonequilibrium Markov processes conditioned on large deviations
type: Item
instance of: scholarly article
title: Nonequilibrium Markov processes conditioned on large deviations
zbMATH Open document ID: 1330.82039
author: R. Chetrite
author: Hugo Touchette
published in: Annales Henri Poincaré
publication date: 2015-09-21T00:00:00Z
full work available at URL: https://arxiv.org/abs/1405.5157
review text: The authors give detailed considerations about the problem of conditioning a Markov process on a rare event. This conditioned process is represented by a conditioning free process that is named the effective or driven process. The whole approach is based on the assumption that the rare event (used in the conditioning) is a large deviation-type event with convex rate function. The driven process is constructed via a generalization of Doob's \(h\)-transform and the authors show that it is equivalent to the conditioned process in the long-time limit. The mentioned equivalence is based on the logarithmic equivalence of path measures. The construction of the driven process allows to prove the equivalence with the so-called exponential tilting of the Markov process. It is used with importance sampling to simulate rare events and giving rise to a non-equilibrium version of the canonical ensemble. The whole paper is divided into six sections and five appendices. After the introduction and a justification of the proposed work, the assumed notations and definitions are presented in Section 2. Then Section 3 discusses the properties of a non-conservative process associated with the canonical path measure study. The authors' approach is based on Doob's transform, thus in Section 4 they present a generalization of this transform that is used in Section 5 to define the driven process. The last section shows possible applications of the proposed approach based on the study of Brownian motion, the Ornstein-Uhlenbeck process, and the problem of quasi-stationary distributions. In the appendices, all necessary details needed in the paper are presented.
reviewed by: Dominik Strzałka
Mathematics Subject Classification ID: 82C31
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 6483691
zbMATH Keywords: non-equilibrium Markov processes
zbMATH Keywords: conditioned Markov processes
zbMATH Keywords: large deviations
zbMATH Keywords: Doob's \(h\)-transform
MaRDI profile type: Publication
OpenAlex ID: W2004018226
arXiv ID: 1405.5157
cites work: Conditional brownian motion and the boundary limits of harmonic functions
cites work: Q3342857
cites work: Q4508926
cites work: Conditioned stochastic differential equations: theory, examples and application to finance.
cites work: Q5436606
cites work: Generalized Gaussian bridges
cites work: Q4477677
cites work: Q4340900
cites work: The Markov processes of Schr�dinger
cites work: Q4872453
cites work: On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains
cites work: On quasi-stationary distributions in absorbing continuous-time finite Markov chains
cites work: Quasi-stationary distributions and population processes
cites work: Quasi-Stationary Distributions
cites work: Quasi-stationary distributions for discrete-state models
cites work: A conditional law of large numbers
cites work: Maximum entropy and conditional probability
cites work: Q4023085
cites work: Sanov property, generalized I-projection and a conditional limit theorem
cites work: Q4391441
cites work: A dozen de Finetti-style results in search of a theory
cites work: Conditional limit theorems for exponential families and finite versions of de Finetti's theorem
cites work: Refinements of the Gibbs conditioning principle
cites work: Conditional limit theorems under Markov conditioning
cites work: Performance analysis conditioned on rare events: an adaptive simulation scheme
cites work: Introduction to rare event simulation.
cites work: Q5538132
cites work: Q4819702
cites work: Exit probabilities and optimal stochastic control
cites work: Advances in filtering and optimal stochastic control. Proceedings of the IFIP-WG 7/1 Working Conference, Cocoyoc, Mexico, February 1-6, 1982
cites work: Q3712220
cites work: Stochastic variational formula for fundamental solutions of parabolic PDE
cites work: On Distributions of Certain Wiener Functionals
cites work: Q3862204
cites work: Q4226355
cites work: Controlled Markov processes and viscosity solutions
cites work: Stochastic control and principal eigenvaluet†
cites work: A remark on the large deviations of an ergodic markov process
cites work: Asymptotic for the principal eigenvalue and eigenfunction of a nearly first-order operator with large potential
cites work: Q3140691
cites work: Risk-Sensitive Control on an Infinite Time Horizon
cites work: Risk-Sensitive and Robust Escape Criteria
cites work: Q3672830
cites work: Handbook of stochastic methods for physics, chemistry and the natural sciences.
cites work: Q4748912
cites work: The Fokker-Planck equation. Methods of solutions and applications.
cites work: Detailed balance has a counterpart in non-equilibrium steady states
cites work: Large Deviations and Ensembles of Trajectories in Stochastic Models
cites work: Thermodynamic formalism for systems with Markov dynamics
cites work: Q3874718
cites work: Q4002759
cites work: Q4223675
cites work: Q4832431
cites work: Non-equilibrium steady states: fluctuations and large deviations of the density and of the current
cites work: Stochastic interacting particle systems out of equilibrium
cites work: Stochastic Processes for Physicists
cites work: Q3066842
cites work: Q5552132

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Continuous-time Markov chains. An applications-oriented approach

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Markov Processes, Brownian Motion, and Time Symmetry

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Lévy Processes and Stochastic Calculus

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Q4937701

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Hypoelliptic second order differential equations

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Q4197841

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Stochastic energetics

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Q5505765

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Non-equilibrium thermodynamics and topology of currents

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: A Learning Algorithm for Risk-Sensitive Cost

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Large deviations

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Q3681702

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Large deviation principle for Markov chains in continuous time

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Large deviations of the empirical flow for continuous time Markov chains

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Penalising Brownian paths. Dedicated to Frank Knight (1933-2007).

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: The equivalence of ensembles for lattice systems: Some examples and a counterexample

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Q3840949

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Equivalence and nonequivalence of ensembles: thermodynamic, macrostate, and measure levels

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: The Many Proofs and Applications of Perron's Theorem

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Two refreshing views of fluctuation theorems through kinematics elements and exponential martingale

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Absolute Continuity of Markov Processes and Generators

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Transformation of Markov processes by multiplicative functionals

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: A technique for exponential change of measure for Markov processes

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Q3397641

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Q3678418

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Irreversible Thermodynamics of Nonlinear Processes and Noise in Driven Systems

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Irreversibility and Generalized Noise

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Q5547508

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Nonequilibrium linear response for Markov dynamics. I: Jump processes and overdamped diffusions

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Nonequilibrium linear response for Markov dynamics. II: Inertial dynamics

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Eulerian and Lagrangian pictures of non-equilibrium diffusions

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Probability of second law violations in shearing steady states

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Dynamical ensembles in stationary states.

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Q4004325

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Brownian motion in a Weyl chamber, non-colliding particles, and random matrices

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Q4451242

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Convex Analysis

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Dynamics of instantaneous condensation in the ZRP conditioned on an atypical current

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Condensation transition in joint large deviations of linear statistics

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: A Brownian-Motion Model for the Eigenvalues of a Random Matrix

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Nonequilibrium statistical mechanics of shear flow: invariant quantities and current relations

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: ASEP on a ring conditioned on enhanced flux

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Transition probabilities and dynamic structure function in the ASEP conditioned on strong flux

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Some limit theorems for absorbing Markov processes

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Large deviations and related problems for absorbing Markov chains

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: Affinity and fluctuations in a mesoscopic noria

Nonequilibrium Markov processes conditioned on large deviations (cites work)
cites work: A Convexity Property in the Theory of Random Variables Defined on a Finite Markov Chain

Nonequilibrium Markov processes conditioned on large deviations (DOI)
DOI: 10.1007/S00023-014-0375-8

Nonequilibrium Markov processes conditioned on large deviations (Recommended article)
Recommended article: Large Deviations in Stationary States, Especially Nonequilibrium
Similarity Score: 0.9256725
Recommender Run: Recommender Run 3

Nonequilibrium Markov processes conditioned on large deviations (Recommended article)
Recommended article: Non-equilibrium thermodynamics of piecewise deterministic Markov processes
Similarity Score: 0.9203713
Recommender Run: Recommender Run 3

Nonequilibrium Markov processes conditioned on large deviations (Recommended article)
Recommended article: Large deviations conditioned on large deviations. I: Markov chain and Langevin equation
Similarity Score: 0.91777396
Recommender Run: Recommender Run 3

Nonequilibrium Markov processes conditioned on large deviations (Recommended article)
Recommended article: Large deviation approach to non-equilibrium processes in stochastic lattice gases
Similarity Score: 0.91363645
Recommender Run: Recommender Run 3

Nonequilibrium Markov processes conditioned on large deviations (Recommended article)
Recommended article: Large deviations for almost Markovian processes
Similarity Score: 0.9128503
Recommender Run: Recommender Run 3

Nonequilibrium Markov processes conditioned on large deviations (Recommended article)
Recommended article: Large deviations for a class of nonhomogeneous Markov chains
Similarity Score: 0.9092054
Recommender Run: Recommender Run 3

Nonequilibrium Markov processes conditioned on large deviations (Recommended article)
Recommended article: Q4003728
Similarity Score: 0.90596735
Recommender Run: Recommender Run 3

Nonequilibrium Markov processes conditioned on large deviations (Recommended article)
Recommended article: Large deviations for coarse grained processes
Similarity Score: 0.9040687
Recommender Run: Recommender Run 3

Nonequilibrium Markov processes conditioned on large deviations (Recommended article)
Recommended article: Large deviations for excursions of non-homogeneous Markov processes
Similarity Score: 0.90151787
Recommender Run: Recommender Run 3

Nonequilibrium Markov processes conditioned on large deviations (Recommended article)
Recommended article: Large deviations for non-Markovian diffusions and a path-dependent Eikonal equation
Similarity Score: 0.90112704
Recommender Run: Recommender Run 3