Strong Invariance Principles for Ergodic Markov Processes

Ardjen Pengel; Joris Bierkens

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arXiv · 2111.12603

Strong Invariance Principles for Ergodic Markov Processes

Ardjen Pengel·Joris Bierkens

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Abstract

Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the 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.

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Ardjen Pengel, Joris Bierkens. 2021-11-24. Strong Invariance Principles for Ergodic Markov Processes. https://arxiv.org/abs/2111.12603

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