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Subordination and self-decomposability
Statistics and Probability Letters, 2001Two facts concerning subordination and self-decomposability are established. It is proved that any subordinated process arizing from a Brownian motion with drift and a self-decomposable subordinator is self-decomposable, and that self-decomposable distributions of type \(G\) are not necessarily of type \(G_L\).
Ken-Iti Sato
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Local Subexponentiality and Self-decomposability
Journal of Theoretical Probability, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Toshiro Watanabe +2 more
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SELF‐DECOMPOSABILITY AND OPTION PRICING
Mathematical Finance, 2006The risk‐neutral process is modeled by a four parameter self‐similar process of independent increments with a self‐decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated.
Yor, Marc +3 more
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A note on self-decomposability of stable process subordinated to self-decomposable subordinator
Statistics & Probability Letters, 2005By aid of an example the author proves the following theorem: There is self-decomposable subordinator \({T(t), t\geq 0}\), and a stable Lévy motion \({X(t), t\geq 0}\), such that the subordinated process \({Y(t)} = {X(T(t)), t \geq 0}\), is not self-decomposable. Then by three remarks the author illuminates this result.
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Multiply self-decomposable probability measures on ?+ and ?+
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1983Self-decomposable probability measures μ on ℝ+ are characterized in terms of minus the logarithm of the Laplace transform of μ, say f, by the requirement that s→sf′(s) is again minus the logarithm of the Laplace transform of an infinitely divisible probability on ℝ+.
Berg, Christian, Forst, Gunnar
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On the Self-Decomposability of Euler's Gamma Function
Lithuanian Mathematical Journal, 2003Let \(\Gamma\) be Euler's gamma function. It is proved that, for all \(\alpha\neq0\), \(\beta>0\), \(\gamma>0\) and \(\delta>0\), the function \(\big[\Gamma(\gamma+i\alpha z)/\Gamma(\gamma)\beta^{i\alpha z}\big]^\delta\) for \(z\in\mathbb{R}\) is a self-decomposable characteristic function from the Thorin class \(\mathcal{T}_e\) and derive its explicit
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