Related papers: Properties of Conditional Expectation Operators an…
In this paper two theorems which describe dissipative boundary conditions for ordinary differential operators on a closed interval are proved. We also show that all these boundary conditions are Birkhoff regular in even case. In odd case…
In this paper, we investigate the convergence of products of conditional expectation operators. We show that if $(\Omega,\cal{F},P)$ is a probability space that is not purely atomic, then divergent sequences of products of conditional…
We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the…
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…
In this paper, we consider the sublinear expectation on bounded random variables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the notion of…
Bayesian properties of the signed root likelihood ratio statistic are analysed. Conditions for first-order probability matching are derived by the examination of the Bayesian posterior and frequentist means of this statistic. Second-order…
Most of the stochastic orders for comparing random variables, considered in the literature, are afflicted with two main drawbacks: (i) lack of connex property and (ii) lack of consideration of any dependence structure between the random…
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to…
In this paper, we describe necessary and sufficient conditions for a binormal or complex symmetric operator to have the other property. Along the way, we find connections to the Duggal and Aluthge transforms, and give further properties of…
Explaining decisions of black-box classifiers is both important and computationally challenging. In this paper, we scrutinize explainers that generate feature-based explanations from samples or datasets. We start by presenting a set of…
New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…
In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
Suppose that $X,Y$ are positive random variable and $m$ a numerical (commutative) mean. We prove that the inequality ${\rm E} (m(X,Y)) \leq m({\rm E} (X), {\rm E} (Y))$ holds if and only if the mean is generated by a concave function. With…
In this paper, we consider conditions that a higher order derivative preserve in conditional expectation operator for a generic nonlinear random variable. Also, the paper introduces higher order derivatives of the Expected Shortfall for a…
The aim of this paper is to give the answer to the problem of characterization of acting conditions (necessary as well as sufficient) for composition operators in some sequence spaces. We also characterize their boundedness and local…
We study the identification of direct and indirect causes on time series and provide conditions in the presence of latent variables, which we prove to be necessary and sufficient under some graph constraints. Our theoretical results and…
Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a marginal domain of attraction condition. An approximation of…
We show that a compact operator $A$ is a multiple of a positive semi-definite operator if and only if $$ \sigma(AB) \subseteq \overline{W(A)W(B)}, \quad\text{for all (rank one) operators $B$}. $$ An example of a normal operator is given to…