On the volume of intersection of three independent Wiener sausages

M. van den Berg

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 2, page 313-337
  • ISSN: 0246-0203

Abstract

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Let K be a compact, non-polar set in ℝm, m≥3 and let SKi(t)={Bi(s)+y: 0≤s≤t, y∈K} be Wiener sausages associated to independent brownian motions Bi, i=1, 2, 3 starting at 0. The expectation of volume of ⋂i=13SKi(t) with respect to product measure is obtained in terms of the equilibrium measure of K in the limit of large t.

How to cite

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van den Berg, M.. "On the volume of intersection of three independent Wiener sausages." Annales de l'I.H.P. Probabilités et statistiques 46.2 (2010): 313-337. <http://eudml.org/doc/239916>.

@article{vandenBerg2010,
abstract = {Let K be a compact, non-polar set in ℝm, m≥3 and let SKi(t)=\{Bi(s)+y: 0≤s≤t, y∈K\} be Wiener sausages associated to independent brownian motions Bi, i=1, 2, 3 starting at 0. The expectation of volume of ⋂i=13SKi(t) with respect to product measure is obtained in terms of the equilibrium measure of K in the limit of large t.},
author = {van den Berg, M.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Wiener sausage; equilibrium measure; Brownian motion},
language = {eng},
number = {2},
pages = {313-337},
publisher = {Gauthier-Villars},
title = {On the volume of intersection of three independent Wiener sausages},
url = {http://eudml.org/doc/239916},
volume = {46},
year = {2010},
}

TY - JOUR
AU - van den Berg, M.
TI - On the volume of intersection of three independent Wiener sausages
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 2
SP - 313
EP - 337
AB - Let K be a compact, non-polar set in ℝm, m≥3 and let SKi(t)={Bi(s)+y: 0≤s≤t, y∈K} be Wiener sausages associated to independent brownian motions Bi, i=1, 2, 3 starting at 0. The expectation of volume of ⋂i=13SKi(t) with respect to product measure is obtained in terms of the equilibrium measure of K in the limit of large t.
LA - eng
KW - Wiener sausage; equilibrium measure; Brownian motion
UR - http://eudml.org/doc/239916
ER -

References

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