In this talk, we present the stochastic local time space integration introduced by Eisenbaum in [2] to the case of Brownian sheet. This allows us to prove a generalised Itô formula for Brownian sheet and derive Davie type inequalities (see [1]) for the Brownian sheet. Such estimates are useful to obtain regularity bounds for some averaging operators along Brownian sheet paths. These operators play a key role in the regularisation by noise theory of ordinary differential equation by random functions.
This is talk is based on a recent joint work with Moustapha Dieye and Olivier Menoukeu Pamen.
[1] A. M. Davie. Uniqueness of solutions of stochastic differential equations. International Mathematics Research Notices, Vol. 2007, 2007. [2] N. Eisenbaum. Integration with respect to local time. Potential analysis, 13(4):303–328, 2000.