학술논문
Stochastic integration with respect to local time of the Brownian sheet and regularising properties of Brownian sheet paths.
Document Type
Journal
Author
Bogso, Antoine-Marie (CM-YND) AMS Author Profile; Dieye, Moustapha (GH-AIMS2) AMS Author Profile; Menoukeu Pamen, Olivier (GH-AIMS2) AMS Author Profile
Source
Subject
60 Probability theory and stochastic processes -- 60G Stochastic processes
60G17Sample path properties
60Probability theory and stochastic processes -- 60J Markov processes
60J55Local time and additive functionals
60J65Brownian motion
60G17
60
60J55
60J65
Language
English
Abstract
Summary: ``In this work, we generalise the stochastic local time space integration introduced in ({\it Potential Anal.} {\bf 13} (2000) 303--328) [MR1804175] to the case of 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.''