| Title:
|
Smoothness for the collision local time of two multidimensional bifractional Brownian motions (English) |
| Author:
|
Shen, Guangjun |
| Author:
|
Yan, Litan |
| Author:
|
Chen, Chao |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
969-989 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\min \{H_{1}K_1,H_{2}K_2\}<{1}/{(d+2)}$. (English) |
| Keyword:
|
bifractional Brownian motion |
| Keyword:
|
collision local time |
| Keyword:
|
intersection local time |
| Keyword:
|
chaos expansion |
| MSC:
|
60G15 |
| MSC:
|
60G18 |
| MSC:
|
60G22 |
| MSC:
|
60J55 |
| MSC:
|
60J65 |
| idZBL:
|
Zbl 1274.60119 |
| idMR:
|
MR3010251 |
| DOI:
|
10.1007/s10587-012-0077-7 |
| . |
| Date available:
|
2012-11-10T21:35:57Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143039 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| . |
