2017/11/28 by Dorival Leão, Leão, Dorival, Alberto Ohashi +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1711.10895
Revised version. To appear in Bulletin des Sciences Mathématiques. arXiv admin note: text overlap with arXiv:1707.04972, arXiv:1408.1423
arxiv created 2018/06/27 · arxiv updated 2018/07/02
In this paper, we establish a universal variational characterization of the non-martingale components associated with weakly differentiable Wiener functionals in the sense of Leão, Ohashi and Simas. It is shown that any Dirichlet process (in particular semimartingales) is a differential form w.r.t Brownian motion driving noise. The drift components are characterized in terms of limits of integral functionals of horizontal-type perturbations and first-order variation driven by a two-parameter occupation time process. Applications to a class of path-dependent rough transformations of Brownian paths under finite p-variation (p≥ 2) regularity is also discussed. Under stronger regularity conditions in the sense of finite (p,q)-variation, the connection between weak differentiability and two-parameter local time integrals in the sense of Young is established.