Smoothness for the collision local time of two multidimensional bifractional Brownian motions
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 969-989.

Voir la notice de l'article dans Czech Digital Mathematics Library

Let $B^{H_{i},K_i}=\{B^{H_{i},K_i}_t, t\geq 0 \}$, $i=1,2$ be two independent, $d$-dimensional bifractional Brownian motions with respective indices $H_i\in (0,1)$ and $K_i\in (0,1]$. Assume $d\geq 2$. One of the main motivations of this paper is to investigate smoothness of the collision local time $$ \ell _T=\int _{0}^{T}\delta (B_{s}^{H_{1},K_1}-B_{s}^{H_{2},K_2}) {\rm d} s, \qquad T>0, $$ where $\delta $ denotes the Dirac delta function. By an elementary method we show that $\ell _T$ is smooth in the sense of Meyer-Watanabe if and only if $\min \{H_{1}K_1,H_{2}K_2\}{1}/{(d+2)}$.
DOI : 10.1007/s10587-012-0077-7
Classification : 60G15, 60G18, 60G22, 60J55, 60J65
Mots-clés : bifractional Brownian motion; collision local time; intersection local time; chaos expansion 
@article{10_1007_s10587_012_0077_7,
     author = {Shen, Guangjun and Yan, Litan and Chen, Chao},
     title = {Smoothness for the collision local time of two multidimensional bifractional {Brownian} motions},
     journal = {Czechoslovak Mathematical Journal},
     pages = {969--989},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {2012},
     doi = {10.1007/s10587-012-0077-7},
     mrnumber = {3010251},
     zbl = {1274.60119},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0077-7/}
}
TY  - JOUR
AU  - Shen, Guangjun
AU  - Yan, Litan
AU  - Chen, Chao
TI  - Smoothness for the collision local time of two multidimensional bifractional Brownian motions
JO  - Czechoslovak Mathematical Journal
PY  - 2012
SP  - 969
EP  - 989
VL  - 62
IS  - 4
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0077-7/
DO  - 10.1007/s10587-012-0077-7
LA  - en
ID  - 10_1007_s10587_012_0077_7
ER  - 
%0 Journal Article
%A Shen, Guangjun
%A Yan, Litan
%A Chen, Chao
%T Smoothness for the collision local time of two multidimensional bifractional Brownian motions
%J Czechoslovak Mathematical Journal
%D 2012
%P 969-989
%V 62
%N 4
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0077-7/
%R 10.1007/s10587-012-0077-7
%G en
%F 10_1007_s10587_012_0077_7
Shen, Guangjun; Yan, Litan; Chen, Chao. Smoothness for the collision local time of two multidimensional bifractional Brownian motions. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 969-989. doi : 10.1007/s10587-012-0077-7. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0077-7/

Cité par Sources :