Stochastic integration with respect to local time of the Brownian sheet and regularising properties of Brownian sheet paths

Abstract: In this work, we generalise the stochastic local time space integration introduced in \cite{Ei00} to the case of Brownian sheet. %We develop a stochastic local time-space calculus with respect to the Brownian sheet. This allows us to prove a generalised two-parameter It^o formula and derive Davie type inequalities for the Brownian sheet. Such estimates are useful to obtain regularity bounds for some averaging type operators along Brownian sheet curves.