A concept of phase asymptotic semiflow is defined. It is shown that any Lagrange stable orbit at which the semiflow is phase asymptotic limits to a stable periodic orbit. A Lagrange stable solution of a C 1 differential equation is considered. When the second compound of the variational equation with respect to this solution is uniformly asymptotically stable and the omega limit set contains no...

This thesis aims to provide a conceptual framework that unifies Leitgeb’s theory of stable beliefs, Battigalli-Siniscalchi’s notion of strong belief and the notions of core, a priori, abnormal and conditional belief studied by Van Fraassen and Arló-Costa. We will first present the difficulties of modeling qualitative notions of belief and belief revision in a quantitative probabilistic setting....

This article describes a propagation scheme for Bayesian networks with conditional Gaussian distributions that does not have the numerical weaknesses of the scheme derived in Lauritzen (1992). The propagation architecture is that of Lauritzen and Spiegelhalter (1988). In addition to the means and variances provided by the previous algorithm , the new propagation scheme yields full local margina...

We utilize recent results concerning a complete axiomatization of stable conditional independence (CI) relative to discrete probability measures to derive perfect model properties of stable CI structures. We show that stable CI can be interpreted as a generalization of undirected graphical models and establish a connection between sets of stable CI statements and propositional formulae in conju...

Motivated by several conjectures posed in the paper "F. Qi and A.-Q. Liu, Completely monotonic degrees for a difference between logarithmic psi functions, J. Comput. Appl. Math., vol. 361, pp. 366--371 (2019); available online at https://doi.org/10.1016/j.cam.2019.05.001", authors compute completely of remainders asymptotic expansions logarithm gamma function digamma function.

We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments,...

Abstract The general problem of constructing regions that have a guaranteed coverage probability for an arbitrary parameter interest $$\psi \in \Psi $$ ψ ∈ Ψ is considered. developed are Bayesian in nature and the probabilities can be considered as conf...

Suppose the variable X to be predicted and the learning sample Y" that was observed have a joint distribution, which depends on an unknown parameter 0. The parameter 0 can be finite or infinite dimensional. A prediction region Dn for X is a random set, depending on Yn, that contains X with prescribed probability a. This paper studies methods for controlling simultaneously the conditional covera...