Abstract
In this article, we consider an m-dimensional stochastic differential equation with coefficients which depend on the maximum of the solution. First, we prove the absolute continuity of the law of the solution. Then we prove that the joint law of the maximum of the ith component of the solution and the i 'th component of the solution is absolutely continuous with respect to the Lebesgue measure in a particular case. The main tool to prove the absolute continuity of the laws is Malliavin calculus.
| Original language | English |
|---|---|
| Pages (from-to) | 2499-2506 |
| Number of pages | 8 |
| Journal | Statistics and Probability Letters |
| Volume | 83 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 2013 Nov |
| Externally published | Yes |
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Keywords
- 60H07
- 60H10
- Absolutely continuous law
- Malliavin calculus
- Stochastic differential equation
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Statistics and Probability
Cite this
Absolute continuity of the laws of a multi-dimensional stochastic differential equation with coefficients dependent on the maximum. / Nakatsu, Tomonori.
In: Statistics and Probability Letters, Vol. 83, No. 11, 11.2013, p. 2499-2506.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Absolute continuity of the laws of a multi-dimensional stochastic differential equation with coefficients dependent on the maximum
AU - Nakatsu, Tomonori
PY - 2013/11
Y1 - 2013/11
N2 - In this article, we consider an m-dimensional stochastic differential equation with coefficients which depend on the maximum of the solution. First, we prove the absolute continuity of the law of the solution. Then we prove that the joint law of the maximum of the ith component of the solution and the i 'th component of the solution is absolutely continuous with respect to the Lebesgue measure in a particular case. The main tool to prove the absolute continuity of the laws is Malliavin calculus.
AB - In this article, we consider an m-dimensional stochastic differential equation with coefficients which depend on the maximum of the solution. First, we prove the absolute continuity of the law of the solution. Then we prove that the joint law of the maximum of the ith component of the solution and the i 'th component of the solution is absolutely continuous with respect to the Lebesgue measure in a particular case. The main tool to prove the absolute continuity of the laws is Malliavin calculus.
KW - 60H07
KW - 60H10
KW - Absolutely continuous law
KW - Malliavin calculus
KW - Stochastic differential equation
UR - http://www.scopus.com/inward/record.url?scp=84882769620&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84882769620&partnerID=8YFLogxK
U2 - 10.1016/j.spl.2013.07.011
DO - 10.1016/j.spl.2013.07.011
M3 - Article
VL - 83
SP - 2499
EP - 2506
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
IS - 11
ER -