Compositions of mappings of infinitely divisible distributions with applications to finding the limits of some nested subclasses
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1. | Title | Title of document | Compositions of mappings of infinitely divisible distributions with applications to finding the limits of some nested subclasses |
2. | Creator | Author's name, affiliation, country | Makoto Maejima; Keio University |
2. | Creator | Author's name, affiliation, country | Yohei Ueda; Keio University |
3. | Subject | Discipline(s) | |
3. | Subject | Keyword(s) | infinitely divisible distribution on ${\mathbb R}^d$, stochastic integral mapping, composition of mappings, limit of nested subclasses |
3. | Subject | Subject classification | 60E07 |
4. | Description | Abstract | Let $\{X_t^{(\mu)},t\ge 0\}$ be a L\'evy process on $R^d$ whose distribution at time 1 is $\mu$, and let $f$ be a nonrandom measurable function on $(0, a), 0 < a\leq \infty$. Then we can define a mapping $\Phi_f(\mu)$ by the law of $\int_0^af(t)dX_t^{(\mu)}$, from $\mathfrak D(\Phi_f)$ which is the totality of $\mu\in I(R^d)$ such that the stochastic integral $\int_0^af(t)dX_t^{(\mu)}$ is definable, into a class of infinitely divisible distributions. For $m\in N$, let $\Phi_f^m$ be the $m$ times composition of $\Phi_f$ itself. Maejima and Sato (2009) proved that the limits $\bigcap_{m=1}^\infty\Phi^m_f(\mathfrak D(\Phi^m_f))$ are the same for several known $f$'s. Maejima and Nakahara (2009) introduced more general $f$'s. In this paper, the limits $\bigcap_{m=1}^\infty\Phi^m_f(\mathfrak D(\Phi^m_f))$ for such general $f$'s are investigated by using the idea of compositions of suitable mappings of infinitely divisible distributions. |
5. | Publisher | Organizing agency, location | |
6. | Contributor | Sponsor(s) | |
7. | Date | (YYYY-MM-DD) | 2010-05-28 |
8. | Type | Status & genre | Peer-reviewed Article |
8. | Type | Type | |
9. | Format | File format | |
10. | Identifier | Uniform Resource Identifier | http://ecp.ejpecp.org/article/view/1557 |
10. | Identifier | Digital Object Identifier | 10.1214/ECP.v15-1557 |
11. | Source | Journal/conference title; vol., no. (year) | Electronic Communications in Probability; Vol 15 |
12. | Language | English=en | |
14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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