Another view on the local time of self-intersections for a function of the Wiener process
Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 119-125.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article is devoted to the local time of self-intersections for the process $F(w),$ where $F: {\mathbb R}^2\to{\mathbb R}^2$ is smooth function, and $w$ is the standard planar Brownian motion. We present the local time of self-intersections for the process $F(w)$ in terms of a manifold.
Keywords: Local time, local time of self-intersections, renormalization of local time.
@article{THSP_2009_15_2_a7,
     author = {O. Izyumtseva},
     title = {Another view on the local time of self-intersections for a function of the {Wiener} process},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {119--125},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a7/}
}
TY  - JOUR
AU  - O. Izyumtseva
TI  - Another view on the local time of self-intersections for a function of the Wiener process
JO  - Teoriâ slučajnyh processov
PY  - 2009
SP  - 119
EP  - 125
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a7/
LA  - en
ID  - THSP_2009_15_2_a7
ER  - 
%0 Journal Article
%A O. Izyumtseva
%T Another view on the local time of self-intersections for a function of the Wiener process
%J Teoriâ slučajnyh processov
%D 2009
%P 119-125
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a7/
%G en
%F THSP_2009_15_2_a7
O. Izyumtseva. Another view on the local time of self-intersections for a function of the Wiener process. Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 119-125. http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a7/

[1] J. S. Rosen, “A renormalized local time for multiple intersections of planar Brownian motion”, Seminaire de Probabilites XX, 1984/85, Lecture Notes in Math., 1204, 1986, 515–531

[2] E. B. Dynkin, “Regularized self-intersection local times of the planar Brownian motion”, Ann. Probab., 16 (1988), 58–74

[3] O. L. Izyumtseva, “The constant of renormalization for the self-intersection local time of diffusion process in the plane”, Ukr. Math. J., 60:11 (2008), 1489–1498

[4] A. Y. Dorogovtsev, Mathematical Analysis, Fact, Kiev, 2004