A stochastic sewing lemma which is applicable for processes taking values in Banach spaces is introduced. Applications to additive functionals of fractional Brownian motion of distributional type are discussed.
The research is supported partly by the Alexander von Humboldt Foundation and the European Research Council under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 683164). Supports from the Hausdorff Research Institute for Mathematics (HIM), where the research was initiated during the junior trimester program in 2019, are acknowledged.
I thank Pavel Zorin-Kranich for various discussions about Proposition 2.4 and the referees for their valuable suggestions.
"Stochastic sewing in Banach spaces." Electron. J. Probab. 28 1 - 22, 2023. https://doi.org/10.1214/23-EJP918