Consider 3-dimensional Brownian motion started on the unit sphere {|x| = 1} with initial density ρ. Let ρt be the first hitting density on the sphere {|x| = t + 1}, t > 0. Then the linear operators Tt defined by Tt ρ = ρt form a semigroup with an infinitesimal generator which is approximately the square root of the Laplacian. This paper studies the analogous situation for Brownian motion with a drift b, where b is small in a suitable scale invariant norm.
@article{urn:eudml:doc:41366,
title = {Fluctuations of brownian motion with drift.},
journal = {Publicacions Matem\`atiques},
volume = {43},
year = {1999},
pages = {85-125},
mrnumber = {MR1697517},
zbl = {0934.60070},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41366}
}
Conlon, Joseph G.; Olsen, Peder. Fluctuations of brownian motion with drift.. Publicacions Matemàtiques, Tome 43 (1999) pp. 85-125. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41366/