Variational formulas for asymptotic variance of general discrete-time Markov chains
نویسندگان
چکیده
The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for central limit theorems. We give variational formulas discrete-time (non-reversible) chains on general state space. provide many applications, extending classical Peskun’s comparison theorem non-reversible and obtaining several theorems between with various perturbations.
منابع مشابه
Asymptotic Variance of Passage Time Estimators in Markov Chains
We consider the problem of estimating passage times in stochastic simulations of Markov chains+ Two types of estimator are considered for this purpose: the “simple” and the “overlapping” estimator; they are compared in terms of their asymptotic variance+ The analysis is based on the regenerative structure of the process and it is shown that when estimating the mean passage time, the simple esti...
متن کاملCLTs and asymptotic variance of time-sampled Markov chains
Abstract: For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel Pμ = ∑ k μ(k)P k. In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker’s and Metropolis algorithms...
متن کاملAsymptotic Variance of Functionals of Discrete- Time Markov Chains via the Drazin Inverse
We consider a ψ-irreducible, discrete-time Markov chain on a general state space with transition kernel P . Under suitable conditions on the chain, kernels can be treated as bounded linear operators between spaces of functions or measures and the Drazin inverse of the kernel operator I−P exists. The Drazin inverse provides a unifying framework for objects governing the chain. This framework is ...
متن کاملHierarchical Counterexamples for Discrete-Time Markov Chains
This paper introduces a novel counterexample generation approach for the verification of discrete-time Markov chains (DTMCs) with two main advantages: (1) We generate abstract counterexamples which can be refined in a hierarchical manner. (2) We aim at minimizing the number of states involved in the counterexamples, and compute a critical subsystem of the DTMC whose paths form a counterexample....
متن کاملVariance Bounding Markov Chains
We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Pesk...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bernoulli
سال: 2023
ISSN: ['1573-9759', '1350-7265']
DOI: https://doi.org/10.3150/21-bej1458