TY - JOUR
T1 - An integral test for the transience of a Brownian path with limited local time
AU - Benjamini, Itai
AU - Berestycki, Nathanael
N1 - PIMS; UBCWe thank Ross Pinsky for some detailed comments improving on a first version of this paper, and Marc Yor for showing us a draft of [13]. N. B. would like to gratefully acknowledge PIMS and UBC, whose support was determinant for the completion of this work, as well as the hospitality of the Weizmann Institute. We would like to thank a first anonymous referee, whose careful reading made us reformulate our results after finding some mistakes in an earlier version.
PY - 2011/5
Y1 - 2011/5
N2 - We study a one-dimensional Brownian motion conditioned on a self-repelling behaviour.Given a nondecreasing positive function f (t), t ≥ 0, consider the measures μt obtained by conditioning a Brownian path so that L s le; f (s),for all s≤ t, where Ls is the local time spent at the origin by time s. It is shown that the measures μt are tight, and that any weak limit of μt as t → ∞ is transient provided that t-3/2 f(t) is integrable. We conjecture that this condition is sharp and present a number of open problems.
AB - We study a one-dimensional Brownian motion conditioned on a self-repelling behaviour.Given a nondecreasing positive function f (t), t ≥ 0, consider the measures μt obtained by conditioning a Brownian path so that L s le; f (s),for all s≤ t, where Ls is the local time spent at the origin by time s. It is shown that the measures μt are tight, and that any weak limit of μt as t → ∞ is transient provided that t-3/2 f(t) is integrable. We conjecture that this condition is sharp and present a number of open problems.
UR - http://www.scopus.com/inward/record.url?scp=79953273523&partnerID=8YFLogxK
U2 - https://doi.org/10.1214/10-AIHP371
DO - https://doi.org/10.1214/10-AIHP371
M3 - مقالة
SN - 0246-0203
VL - 47
SP - 539
EP - 558
JO - Annales De L Institut Henri Poincare-Probabilites Et Statistiques
JF - Annales De L Institut Henri Poincare-Probabilites Et Statistiques
IS - 2
ER -