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 Itô 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.

26 pages

References in corpus (2)

• Path-by-path uniqueness of multidimensional SDE's on the plane with nondecreasing coefficients
• Stochastic integration with respect to local time of the Brownian sheet and regularising properties of Brownian sheet paths

Cited by in corpus (2)

• Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts
• Stochastic integration with respect to local time of the Brownian sheet and regularising properties of Brownian sheet paths