We consider additive functionals of stationary Markov processes and show that under Kipnis–
Varadhan type conditions they converge in rough path topology to a Stratonovich Brownian …

Functional central limit theorems for random processes viewed as rough paths were
obtained in a wide range of models and settings in recent years. Each result of this kind has …

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 …