Related papers: Completely Random Measures and L\'evy Bases in Fre…
We say that a finitely additive probability measure $\mu$ on $\omega$ is \emph{a P-measure} if it vanishes on points and for each decreasing sequence $(E_n)$ of infinite subsets of $\omega$ there is $E\subseteq\omega$ such that…
Quantum measurements can produce randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement…
We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and…
Let $\mu$ be a probability measure (or corresponding random variable) such that all moments $\mu_n$ exist. Knowledge of the moments is not sufficient to determine infinite divisibility of the measure; we show also that infinitely divisible,…
Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent.
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the 'general tension-reduction' (GTR) model, able to describe general quantum-like measurements with an arbitrary number of…
Determinism is established in quantum mechanics by tracing the probabilities in the Born rules back to the absolute (overall) phase constants of the wave functions and recognizing these phase constants as pseudorandom numbers. The reduction…
Based on the theory of independently scattered random measures, we introduce a natural generalisation of Gaussian space-time white noise to a Levy-type setting, which we call Levy-valued random measures. We determine the subclass of…
The celebrated L\'evy--Khintchine theorem is a fundamental limiting law that describes the growth rate of the denominators of the convergents in the continued fraction expansion of a Lebesgue-typical real number. In a recent breakthrough,…
We generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantum probability measure is a weak*-closed convex set of…
A general theory of resource-bounded measurability and measure is developed. Starting from any feasible probability measure $\nu$ on the Cantor space $\C$ and any suitable complexity class $C \subseteq \C$, the theory identifies the subsets…
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…
Given a stochastic process $\{A_n, n \geq 1\}$ taking values in natural numbers, the random continued fractions is defined as $[A_1, A_2, \cdots, A_n, \cdots]$ analogue to the continued fraction expansion of real numbers. Assume that…
A quasi-infinitely divisible distribution on $\mathbb{R}^d$ is a probability distribution $\mu$ on $\mathbb{R}^d$ whose characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible…
For continuous maps on a compact manifold M, particularly for those that do not preserve the Lebesgue measure m, we define the observable invariant probability measures as a generalization of the physical measures. We prove that any…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
A scaling on some space is a measurable action of the group of positive real numbers. A measure on a measurable space equipped with a scaling is said to be $\alpha$-homogeneous for some nonzero real number $\alpha$ if the mass of any…
We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally…