For a Brownian sheet on the nonnegative quadrant, we show that any
nontrivial curve in the quadrant with the property that the Brownian sheet
restricted to the curve gives rise to a differentiable function cannot be
differentiable at any point. This result has several implications for level
sets of the Brownian sheet. In particular, any Jordan arc contained in a level
set must be nowhere differentiable.
Publié le : 1996-01-14
Classification:
Brownian sheet,
level sets,
nondifferentiability,
Jordan arc,
60G60,
60G15
@article{1042644712,
author = {Dalang, Robert C. and Mountford, T.},
title = {Nondifferentiability of curves on the Brownian sheet},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 182-195},
language = {en},
url = {http://dml.mathdoc.fr/item/1042644712}
}
Dalang, Robert C.; Mountford, T. Nondifferentiability of curves on the Brownian sheet. Ann. Probab., Tome 24 (1996) no. 2, pp. 182-195. http://gdmltest.u-ga.fr/item/1042644712/