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Self-Decomposable Laws from Continuous Branching Processes
Journal of Theoretical Probability, 2019A continuous-time and space branching process (CBP) is a Markov process \((Z_t : t \geq 0)\) taking value in \([0,\infty]\) that satisfies the branching property, i.e., that the process starting from \(z_1 + z_2\) can be constructed as the sum of two independent copies of the same process, starting from \(z_1\) and \(z_2\) respectively.
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Stable and Semistable Hemigroups: Domains of Attraction and Self-Decomposability
Journal of Theoretical Probability, 2003The author obtains descriptions of stable and semi-stable convolution hemigroups as limits in certain functional limit theorems for operator-normed sequences of independent random vectors (not necessarily identically distributed). This functional limit law is closely related to a limit law of infinitesimal triangular arrays of random vectors, which ...
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A characterization of self-decomposable probabilities on the half-line
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1979It is shown that a probability measure μ on ℝ+ is self-decomposable if and only if for s>0 the sequence $$\left( {\frac{1}{{n!}}\mathop \smallint \limits_0^\infty e^{ - ts} (ts)^n d\mu (t)} \right)_{n \geqq 0} ,$$ determines a probability on ℕ0, that is self-decomposable in the sense of Steutel and van Harn.
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Solution to Stein’s Equation for Self-Decomposable Laws
2019Having found in Chap. 3 that the operator \(\mathcal{A}_{{\text {gen}}}\) given for all \(f\in BLip(\mathbb R)\), by $$\begin{aligned}\mathcal{A}_{{\text {gen}}} f(x)=xf(x)-bf(x)-\int ^{+\infty }_{-\infty } (f(x+u)-f(x) {1\!\!1}_{|u|\le 1})u\nu (du), \end{aligned}$$ characterizes \(X\sim ID(b, 0,\nu )\), the usual next step in Stein’s method is ...
Benjamin Arras, Christian Houdré
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On certain self-decomposable distributions
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1977Shanbhag, D. N., Sreehari, M.
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Drought effects on root and shoot traits and their decomposability
Functional Ecology, 2023Laura Reinelt +2 more
exaly
Self-decomposability of weak variance generalised gamma convolutions
Stochastic Processes and Their Applications, 2020Boris Buchmann +2 more
exaly

