• 15h30 - Alberto OHASHI (Universidade de Brasilia)

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

ABSTRACT.

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.