TY - JOUR
T1 - Proof of a tanaka-like formula stated by J. Rosen in seminaire XXXVIII
AU - Markowsky, Gregory
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
UR - http://www.springerlink.com/content/978-3-540-77912-4#section=254500&page=1&locus=0
U2 - 10.1007/978-3-540-77913-1_9
DO - 10.1007/978-3-540-77913-1_9
M3 - Article
SN - 0075-8434
VL - 1934
SP - 199
EP - 202
JO - Lecture Notes in Mathematics
JF - Lecture Notes in Mathematics
ER -