Results 191 to 200 of about 488 (215)
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Supremum self-decomposable random vectors
Probability Theory and Related Fields, 1986An \({\bar {\mathbb{R}}}^ d\)-valued random variable X is said to be sup selfdecomposable if for each \(t>0\) there is an \({\bar {\mathbb{R}}}^ d\)- valued random variable \(X_ t\) independent of X such that \[ (1)\quad X=^{d}(X-t\cdot 1)\vee X_ t, \] where \(=^{d}\) means equality in distribution and \(\vee\) means componentwise supremum.
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Self-decomposability on ℝ and ℤ
1984The set L(ℝ) of self-decomposable probability measures on ℝ is studied in terms of characteristic functions using a certain differential operator and its inverse. In particular a natural bijection onto L(ℝ), introduced by Wolfe, is interpreted via these operators.
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Semi-self-decomposable distributions on Z+
Annals of the Institute of Statistical Mathematics, 2007We present a notion of semi-self-decomposability for distributions with support in Z+. We show that discrete semi-self-decomposable distributions are infinitely divisible and are characterized by the absolute monotonicity of a specific function. The class of discrete semi-self-decomposable distributions is shown to contain the discrete semistable ...
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Self-decomposable discrete distributions and branching processes
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1981Self-decomposable distributions are known to be absolutely continuous. In this note analogues of the concept of self-decomposability are proposed for distributions on the set ℕ0 of nonnegative integers. To each of them corresponds an analogue of multiplication (in distribution) that preserves ℕ0-valuedness and is characterized by a composition ...
Harn, van, K. +2 more
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Probability and Statistics: Self-Decomposability, Finance and Turbulence
1998After some general remarks about the relationship between probability and statistics, a discussion is given of closely similar, key features of empirical data from finance and from turbulence, and this is followed by an account of recent work on stochastic modelling incorporating those features.
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Self decomposability and option pricing
2007The 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.
Geman, Helyette +1 more
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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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