Proof of a tanaka-like formula stated by J. Rosen in seminaire XXXVIII

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Abstract

Let B_t be a one dimensional Brownian motion, and let alphaa?? denote the derivative of the intersection local time of B_t as defined by J. Rosen in [2]. The object of this paper is to prove the following formula 1/2 _t(x)+ 1/2 sgn(x)t= int_superscript_t_0 L_superscript_(B_s - x) dB_s - 1/2 int_superscript_t_0 sgn(B_t - B_u - x)du (1) which was given as a formal identity in [2] without proof.
Original languageEnglish
Pages (from-to)199 - 202
Number of pages4
JournalLecture Notes in Mathematics
Volume1934
DOIs
Publication statusPublished - 2008
Externally publishedYes

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