Strong invariance principles for ergodic Markov processes

Pengel, A.L.; Bierkens, G.N.J.C.

doi:10.1214/23-EJS2199

Strong invariance principles for ergodic Markov processes

Title

Strong invariance principles for ergodic Markov processes

Author

Pengel, A.L. (TU Delft Statistics)
Bierkens, G.N.J.C. (TU Delft Statistics)

Date

2024

Abstract

Strong invariance principles describe the error term of a Brownian approximation to the partial sums of a stochastic process. While these strong approximation results have many applications, results for continuous-time settings have been limited. In this paper, we obtain strong invariance principles for a broad class of ergodic Markov processes. Strong invariance principles provide a unified framework for analysing commonly used estimators of the asymptotic variance in settings with a dependence structure. We demonstrate how this can be used to analyse the batch means method for simulation output of Piecewise Deterministic Monte Carlo samplers. We also derive a fluctuation result for additive functionals of ergodic diffusions using our strong approximation results.

Subject

asymptotic variance estimation
piecewise deterministic Markov processes
Strong invariance principle

To reference this document use:

http://resolver.tudelft.nl/uuid:a48c1478-abfd-4fa1-86b0-0b1ddff9a3b6

DOI

https://doi.org/10.1214/23-EJS2199

ISSN

1935-7524

Source

Electronic Journal of Statistics, 18 (1), 191-246

Part of collection

Institutional Repository