WIAS Preprint No. 2809, (2021)

Rough invariance principle for delayed regenerative processes


  • Orenshtein, Tal

2020 Mathematics Subject Classification

  • 60K37 60F17 82C41 82B43


  • Invariance principle, rough paths, $p$-variation, area anomaly, regenerative process, key renewal theorem, random walks in random environment




We derive an invariance principle for the lift to the rough path topology of stochastic processes with delayed regenerative increments under an optimal moment condition. An interesting feature of the result is the emergence of area anomaly, a correction term in the second level of the limiting rough path which is identified as the average stochastic area on a regeneration interval. A few applications include random walks in random environment and additive functionals of recurrent Markov chains. The result is formulated in the p-variation settings, where a rough Donsker Theorem is available under the second moment condition. The key renewal theorem is applied to obtain an optimal moment condition.

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