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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.
 
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7. Date (YYYY-MM-DD) 2010-05-28
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
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
 
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