Rough invariance principle for delayed regenerative processes

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