Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities

DOI10.1137/19M1237429zbMath1501.47073arXiv1812.05174MaRDI QIDQ4961000

Luc Rey-Bellet, Jeremiah Birrell

Publication date: 24 April 2020

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.05174

zbMATH Keywords

relative entropyBernstein inequalityMarkov processPoincaré inequalityuncertainty quantificationLiapunov function\(\log\)-Sobolev inequality

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Markov semigroups and applications to diffusion processes (47D07) Large deviations (60F10) Systems of functional equations and inequalities (39B72)

Related Items (5)

Model Uncertainty and Correctability for Directed Graphical Models ⋮ Overcoming the timescale barrier in molecular dynamics: Transfer operators, variational principles and machine learning ⋮ Uncertainty Quantification for Markov Random Fields ⋮ Large deviations of empirical measures of diffusions in weighted topologies ⋮ Quantification of model uncertainty on path-spaceviagoal-oriented relative entropy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability of noisy Metropolis-Hastings
• Poincaré inequality and the \(L^{p}\) convergence of semi-groups
• Hypocoercivity for kinetic equations with linear relaxation terms
• A simple proof of the Poincaré inequality for a large class of probability measures
• Large deviations techniques and applications.
• Lower bounds for eigenvalues of regular Sturm-Liouville operators and the logarithmic Sobolev inequality
• Comparison theorems for reversible Markov chains
• A deviation inequality for non-reversible Markov processes
• Scalable information inequalities for uncertainty quantification
• Perturbation theory for Markov chains via Wasserstein distance
• Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates
• Transportation-information inequalities for Markov processes
• Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré
• A short course on operator semigroups
• Logarithmic Sobolev inequalities for finite Markov chains
• Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels
• MEASURING DISTRIBUTION MODEL RISK
• Path-Space Information Bounds for Uncertainty Quantification and Sensitivity Analysis of Stochastic Dynamics
• Robust Sensitivity Analysis for Stochastic Systems
• Robust risk measurement and model risk
• Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
• Bernstein-type Concentration Inequalities for Symmetric Markov Processes
• Information Metrics For Long-Time Errors in Splitting Schemes For Stochastic Dynamics and Parallel Kinetic Monte Carlo
• Matrix-Exponential Distributions in Applied Probability
• On Divergences and Informations in Statistics and Information Theory
• Chernoff and Berry–Esséen inequalities for Markov processes
• On the entropy for semi-Markov processes
• Examples of fitting structured phase–type distributions
• Regular Perturbation of V-Geometrically Ergodic Markov Chains
• How Biased Is Your Model? Concentration Inequalities, Information and Model Bias
• Hypocoercivity for linear kinetic equations conserving mass
• Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification
• Binomial-Poisson entropic inequalities and the M/M/∞queue
• deviation bounds for additive functionals of markov processes
• Sensitivity and convergence of uniformly ergodic Markov chains
• Applied Semi-Markov Processes
• Semi-Markov processes and reliability

This page was built for publication: Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities