• Corpus ID: 235265774

Variational principles for asymptotic variance of general Markov processes

@inproceedings{Huang2021VariationalPF,
  title={Variational principles for asymptotic variance of general Markov processes},
  author={Lu-Jing Huang and Yonghua Mao and Tao Wang},
  year={2021}
}
A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get a upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and nonreversible diffusion processes. 

References

SHOWING 1-10 OF 30 REFERENCES
Variational Formulas of Asymptotic Variance for General Discrete-time Markov Chains
The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for the central limit theorems. We give the variational formulas for the asymptotic variance
Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
We prove a functional central limit theorem for additive functionals of stationary reversible ergodic Markov chains under virtually no assumptions other than the necessary ones. We use these results
The central limit theorem for Markov chains with normal transition operators, started at a point
Abstract. The central limit theorem and the invariance principle, proved by Kipnis and Varadhan for reversible stationary ergodic Markov chains with respect to the stationary law, are established
Variance 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.
Variational principles of the exit time for Hunt processes generated by semi-Dirihclet forms.
We give the variational principles of the exit time from an open set of the Hunt process generated by a regular lower bounded semi-Dirichlet form. For symmetric Markov processes, variational formulas
Geometric Ergodicity and Hybrid Markov Chains
Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a
Improving the Asymptotic Performance of Markov Chain Monte-Carlo by Inserting Vortices
TLDR
It is confirmed that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.
On the central limit theorem for geometrically ergodic Markov chains
Abstract.Let X0,X1,... be a geometrically ergodic Markov chain with state space and stationary distribution π. It is known that if h:→ R satisfies π(|h|2+ɛ)<∞ for some ɛ>0, then the normalized sums
Minimising MCMC variance via diffusion limits, with an application to simulated tempering
We derive new results comparing the asymptotic variance of diffusions by writing them as appropriate limits of discrete-time birth–death chains which themselves satisfy Peskun orderings. We then
Accelerating reversible Markov chains
Reversibility is usually applied in most popular Markov chain Monte Carlo algorithms, such as the Metropolis–Hastings algorithm and the Gibbs sampler. However, several researchers have shown that
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