Seminar Probabilités-Statistiques-Contrôle

Event type:
Event name:
Start at:
november 22, 2021
Salle 2320, UMA
Responsible team:
Stochastic Analysis (in cooperation with CMAP, ENSAE)
  • 15h30 - Alberto OHASHI (Universidade de Brasilia)

Rough paths and Stratonovich integrals driven by covariance singular Gaussian processes.


In this talk, we present the relation between a stochastic version of the rough path integral with the symmetric-Stratonovich integral driven by a class of Gaussian processes with singular covariance structure. Under mild regularity conditions in the sense of Malliavin calculus, we establish equivalence between stochastic rough path and symmetric-Stratonovich integrals. As a by-product, we express the difference between the stochastic rough and Skorohod integral as a trace component specified in terms of Malliavin derivatives for possibly anticipative processes. We provide a sufficient condition for the existence of the stochastic rough path integral beyond pathwise H"older continuity found in controlled rough path theory.