Abstract
Let be a fractional Brownian motion on with Hurst parameter and let F be its pathwise antiderivative (so F is a differentiable random function such that ) with . Let B be a standard Brownian motion, independent of . We show that the zero energy part of has positive and finite p-th variation in a special sense for . We also present some simulation results about the zero energy part of a certain median process which suggest that its -th variation is positive and finite.
Citation
László Bondici. Vilmos Prokaj. "Example of a Dirichlet process whose zero energy part has finite p-th variation." Electron. Commun. Probab. 28 1 - 13, 2023. https://doi.org/10.1214/23-ECP558
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