相关论文: What is Stochastic Independence?

There has for longer been an interest in finding equivalent conditions which define inner product spaces, and the respective literature is considerable, see for instance Amir, which lists 350 such results. Here, in this tradition, an…

In [2] the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness…

The current definition of a conditional probability distribution enables one to update probabilities only on the basis of stochastic information. This paper provides a definition for conditional probability distributions with non-stochastic…

Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…

Statistical dependence measures like mutual information is ideal for analyzing autoencoders, but it can be ill-posed for deterministic, static, noise-free networks. We adopt the variational (Gaussian) formulation that makes dependence among…

Investigation of the reversibility of the directional hierarchy in the interdependency among the notions of conditional independence, conditional mean independence, and zero conditional covariance, for two random variables X and Y given a…

Semi-automata are abstractions of electronic devices that are deterministic finite-state machines having inputs but no outputs. Generalized semiautomata are obtained from stochastic semiautomata by dropping the restrictions imposed by…

Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…

Critical parts of the definitions of standard serial and standard parallel modes refer to stochastic independence. Standard serial models are defined by stochastic independence and identical distributions of their processing times.…

We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…

Intuitive Set Theory (IST) is defined as the theory we get, when we add Axiom of Monotonicity and Axiom of Fusion to Zermelo-Fraenkel set theory. In IST, Continuum Hypothesis is a theorem, Axiom of Choice is a theorem, Skolem paradox does…

We discuss the construction of component importance measures for binary coherent reliability systems from known stochastic dependence measures by measuring the dependence between system and component failures. We treat both the…

The concept of impedance, which characterises the current response to a periodical driving, is introduced in the context of stochastic transport. In particular, we calculate the impedance for an exactly solvable model, namely the stochastic…

A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…

It is well known that conditional independence can be used to factorize a joint probability into a multiplication of conditional probabilities. This paper proposes a constructive definition of inter-causal independence, which can be used to…

The aim of this note is to introduce a notion of dynamical entropy, which we call infinite-product entropy, for probability measures on (countable) infinite cartesian product of any measurable space with itself. The idea behind the…

We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator.…

Entanglement is a quantum resource, in some ways analogous to randomness in classical computation. Inspired by recent work of Gheorghiu and Hoban, we define the notion of "pseudoentanglement'', a property exhibited by ensembles of…

We introduce and study a new notion of non-commutative independence, called V-monotone independence, which can be viewed as an extension of the monotone independence of Muraki. We investigate the combinatorics of mixed moments of V-monotone…

We investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant…