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.
Original language | English |
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Pages (from-to) | 191-246 |
Number of pages | 56 |
Journal | Electronic Journal of Statistics |
Volume | 18 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2024 |
Keywords
- asymptotic variance estimation
- piecewise deterministic Markov processes
- Strong invariance principle