Related papers: A note on tempered measures
Information theory is widely accepted as a powerful tool for analyzing complex systems and it has been applied in many disciplines. Recently, some central components of information theory - multivariate information measures - have found…
We study properties of temperate non-negative purely atomic measures in the Euclidean space such that the distributional Fourier transform of these measures are pure point ones. A connection between these measures and almost periodicity is…
This short note contains some definitions and formulas about the power of an observable in statistically separating different classes of events.
We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.
Meyer defined crystalline measures as tempered distributions $\mu$ such that both $\mu$ and its Fourier transform $\widehat\mu$ are pure-point Radon measures of locally finite support. He conjectured that every crystalline measure is almost…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
Tempered Exponential Measures (TEMs) are a parametric generalization of the exponential family of distributions maximizing the tempered entropy function among positive measures subject to a probability normalization of their power…
Term weighting metrics assign weights to terms in order to discriminate the important terms from the less crucial ones. Due to this characteristic, these metrics have attracted growing attention in text classification and recently in…
In the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is remarkably efficient and allows a solution in a few…
For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…
This short note describes a connection between algorithmic dimensions of individual points and classical pointwise dimensions of measures.
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
In various research areas related to decision making, problems and their solutions frequently rely on certain functions being monotonic. In the case of non-monotonic functions, one would then wish to quantify their lack of monotonicity. In…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
A simple condition is given that is sufficient to determine whether a measure that is absolutely continuous with respect to a Gau{\ss}ian measure on the space of distributions is reflection positive. It readily generalises conventional…
Estimates of densities of convolution semigroups of probability measures are given under specific assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent. The assumptions are satisfied, e.g., by tempered stable…
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured…
Weak measurement is a standard measuring procedure with two changes: it is performed on pre- and post-selected quantum systems and the coupling to the measuring device is weakened. The outcomes of weak measurements, ``weak values'' are very…