Self-decomposable probability distributions on $R^m$

Kazimierz Urbanik

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On sufficiency of decomposable jets in $J^{r} (2, 1)$

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On inhomogeneous self-similar measures and their $L^{q}$ spectra

Przemysław Liszka (2013)

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Let $S_{i} : ℝ^{d} \to ℝ^{d}$ for i = 1,..., N be contracting similarities, let $(p ₁, . . ., p_{N}, p)$ be a probability vector and let ν be a probability measure on $ℝ^{d}$ with compact support. It is well known that there exists a unique inhomogeneous self-similar probability measure μ on $ℝ^{d}$ such that $μ = \sum_{i = 1}^{N} p_{i} μ \circ S_{i}^{- 1} + p ν$ . We give satisfactory estimates for the lower and upper bounds of the $L^{q}$ spectra of inhomogeneous self-similar measures. The case in which there are a countable number of contracting similarities and probabilities is considered. In particular,...

On a fixobject property for $l^{c} β$ -semigroupoids

M. Đurić (1973)

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Order relations in the set of probability distribution functions and their applications in queueing theory

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CONTENTSIntroduction......................................................................................................................................... 51. n-Monotonic functions on (— ∞, ∞)........................................................................................... 62. Order relations in the set of probability distribution functions....................................................... 12 2.1. Preliminary concepts...............................................................................................................

On spirallike functions of order $α$ and type $β$ with fixed second coefficient

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Properties of unique information

Johannes Rauh, Maik Schünemann, Jürgen Jost (2021)

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We study the unique information function $U I (T : X ∖ Y)$ defined by Bertschinger et al. within the framework of information decompositions. In particular, we study uniqueness and support of the solutions to the convex optimization problem underlying the definition of $U I$ . We identify sufficient conditions for non-uniqueness of solutions with full support in terms of conditional independence constraints and in terms of the cardinalities of $T$ , $X$ and $Y$ . Our results are based on a reformulation of the first...