Continuous differentiability of renormalized intersection local times in R1

We study γk(x2, …, xk; t), the k-fold renormalized self-intersection local time for Brownian motion in R1. Our main result says that γk(x2, …, xk; t) is continuously differentiable in the spatial variables, with probability 1.

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Bibliographic Details
Published inAnnales de l'I.H.P. Probabilités et statistiques Vol. 46; no. 4; pp. 1025 - 1041
Main Author Rosen, Jay S.
Format Journal Article
LanguageEnglish
Published Institut Henri Poincaré 01.11.2010
Subjects
60J55
60J65
Brownian motion
Continuous differentiability
Intersection local time
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Summary:We study γk(x2, …, xk; t), the k-fold renormalized self-intersection local time for Brownian motion in R1. Our main result says that γk(x2, …, xk; t) is continuously differentiable in the spatial variables, with probability 1.
ISSN:0246-0203
DOI:10.1214/09-AIHP338